解決35*1-1/(1.035)^36/0.035+1000/(1.035)^30 |Microsoft數學求解器

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

評估

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

解題步驟

計算 1.035 的 36 乘冪，然後得到 3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625。

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

同時對分子與分母乘上 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 以展開 \frac{1}{3.450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625}。

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

透過找出與消去 14551915228366851806640625，對分式 \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{3450266111455967907325786350602725936443778990709405243289294726555537040915296110339113511145114898681640625} 約分至最低項。

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

將 1 轉換成分數 \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}。

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

因為 \frac{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 和 \frac{68719476736000000000000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 的分母相同，所以將分子相減即可相減這兩個值。

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

從 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 減去 68719476736000000000000000000000000000000000000000000000000000000000000000000000000 會得到 168381005043207569695836979093150364567632084923980533752615109079380709095164971201。

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

運算式 \frac{\frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201}}{0.035} 為最簡分數。

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

將 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 乘上 0.035 得到 8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035。

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

同時對分子與分母乘上 1000 以展開 \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992.035}。

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

透過找出與消去 35，對分式 \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{8298516862272264939354294268260262759867122972339318681341528817778324818330773992035} 約分至最低項。

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

運算式 35\times \frac{4810885858377359134166770831232867559075202426399443821503288830839448831290427748600}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 為最簡分數。

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

將 35 乘上 4810885858377359134166770831232867559075202426399443821503288830839448831290427748600 得到 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000。

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

計算 1.035 的 30 乘冪，然後得到 2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625。

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

同時對分子與分母乘上 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 以展開 \frac{1000}{2.806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625}。

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

透過找出與消去 931322574615478515625，對分式 \frac{1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}{2806793704702633616983891832168892979806961373469044108382206494831711985170841217041015625} 約分至最低項。

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

237100481779207569695836979093150364567632084923980533752615109079380709095164971201 和 3013771792079123197504001394491729024198721873046196628470764090905249 的最小公倍數為 237100481779207569695836979093150364567632084923980533752615109079380709095164971201。將 \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 和 \frac{1073741824000000000000000000000000000000000000000000000000000000000000000}{3013771792079123197504001394491729024198721873046196628470764090905249} 轉換為分母是 237100481779207569695836979093150364567632084923980533752615109079380709095164971201 的分數。

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

因為 \frac{168381005043207569695836979093150364567632084923980533752615109079380709095164971201000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 和 \frac{84473782801336029413376000000000000000000000000000000000000000000000000000000000000000}{237100481779207569695836979093150364567632084923980533752615109079380709095164971201} 的分母相同，所以將分子相加即可相加這兩個值。

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

將 168381005043207569695836979093150364567632084923980533752615109079380709095164971201000 與 84473782801336029413376000000000000000000000000000000000000000000000000000000000000000 相加可以得到 252854787844543599109212979093150364567632084923980533752615109079380709095164971201000。

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