Leysa 35*1-1/(1.035)^36/0.035+1000/(1.035)^30

$$35 \times \frac { 1 - \frac { 1 } { ( 1.035 ) ^ { 36 } } } { 0.035 } + \frac { 1000 } { ( 1.035 ) ^ { 30 } }$$

Meta

$$\frac{252854787844543599109212979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}\approx 1066.445694024$$

Lausnarskref

Reiknaðu 1.035 í 36. veldi og fáðu 3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625.

$$35\times \frac{1-\frac{1}{3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625}}{0.035}+\frac{1000}{1.035^{30}}$$

Leystu upp \frac{1}{3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625} með því að margfalda bæði teljara og nefnara með 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$35\times \frac{1-\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625}}{0.035}+\frac{1000}{1.035^{30}}$$

Minnka brotið \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625} eins mikið og hægt er með því að draga og stytta út 14551915228366851806640625.

$$35\times \frac{1-\frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Breyta 1 í brot \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}.

$$35\times \frac{\frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}-\frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Þar sem \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} og \frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} eru með sama nefnara skaltu draga frá með því að nota frádrátt á teljarana.

$$35\times \frac{\frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201-68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Dragðu 68719476736000000000000000000000000000000000000000000000000000000000000000000000000 frá 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 til að fá út 168381005043207569695836979093150364567632084923980533752615109079380709095164971201.

$$35\times \frac{\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035}+\frac{1000}{1.035^{30}}$$

Sýndu \frac{\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035} sem eitt brot.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201\times 0.035}+\frac{1000}{1.035^{30}}$$

Margfaldaðu 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 og 0.035 til að fá út 8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035}+\frac{1000}{1.035^{30}}$$

Leystu upp \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035} með því að margfalda bæði teljara og nefnara með 1000.

$$35\times \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992035}+\frac{1000}{1.035^{30}}$$

Minnka brotið \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992035} eins mikið og hægt er með því að draga og stytta út 35.

$$35\times \frac{4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Sýndu 35\times \frac{4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} sem eitt brot.

$$\frac{35\times 4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Margfaldaðu 35 og 4810885858377359134166770831232867559075202426399443821503288830839448831290427748600 til að fá út 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{1.035^{30}}$$

Reiknaðu 1.035 í 30. veldi og fáðu 2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000}{2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625}$$

Leystu upp \frac{1000}{2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625} með því að margfalda bæði teljara og nefnara með 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625}$$

Minnka brotið \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625} eins mikið og hægt er með því að draga og stytta út 931322574615478515625.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{1073741824000000000000000000000000000000000000000000000000000000000000000}{3013771792079123197504001394491729024198721873046196628470764090905249}$$

Sjaldgæfasta margfeldi 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 og 3013771792079123197504001394491729024198721873046196628470764090905249 er 237100481779207569695836979093150364567632084923980533752615109079380709095164971201. Breyttu \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} og \frac{1073741824000000000000000000000000000000000000000000000000000000000000000}{3013771792079123197504001394491729024198721873046196628470764090905249} í brot með nefnaranum 237100481779207569695836979093150364567632084923980533752615109079380709095164971201.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}+\frac{84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$

Þar sem \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} og \frac{84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} eru með sama nefnara skaltu leggja saman með því að leggja saman teljarana.

$$\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000+84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$

Leggðu saman 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000 og 84473782801336029413376000000000000000000000000000000000000000000000000000000000000000 til að fá 252854787844543599109212979093150364567632084923980533752615109079380709095164971201000.

$$\frac{252854787844543599109212979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}$$