Leysa A=30000.011.01^24/1.01^24-1

$$A = 3000 \frac{ 0.01 { 1.01 }^{ 24 } }{ { 1.01 }^{ 24 } -1 }$$

Leystu fyrir A

$$A = \frac{12697346485319144689037148804934554221046267624010}{89911549510638156301238293497818474034875587467} = 141\frac{1.9818004319164138 \times 10^{46}}{8.991154951063816 \times 10^{46}} \approx 141.22041667$$

Skref til að leysa línulega jöfnu

Reiknaðu 1.01 í 24. veldi og fáðu 1.269734648531914468903714880493455422104626762401.

$$A=3000\times \frac{0.01\times 1.269734648531914468903714880493455422104626762401}{1.01^{24}-1}$$

Margfaldaðu 0.01 og 1.269734648531914468903714880493455422104626762401 til að fá út 0.01269734648531914468903714880493455422104626762401.

$$A=3000\times \frac{0.01269734648531914468903714880493455422104626762401}{1.01^{24}-1}$$

Reiknaðu 1.01 í 24. veldi og fáðu 1.269734648531914468903714880493455422104626762401.

$$A=3000\times \frac{0.01269734648531914468903714880493455422104626762401}{1.269734648531914468903714880493455422104626762401-1}$$

Dragðu 1 frá 1.269734648531914468903714880493455422104626762401 til að fá út 0.269734648531914468903714880493455422104626762401.

$$A=3000\times \frac{0.01269734648531914468903714880493455422104626762401}{0.269734648531914468903714880493455422104626762401}$$

Leystu upp \frac{0.01269734648531914468903714880493455422104626762401}{0.269734648531914468903714880493455422104626762401} með því að margfalda bæði teljara og nefnara með 100000000000000000000000000000000000000000000000000.

$$A=3000\times \frac{1269734648531914468903714880493455422104626762401}{26973464853191446890371488049345542210462676240100}$$

Sýndu 3000\times \frac{1269734648531914468903714880493455422104626762401}{26973464853191446890371488049345542210462676240100} sem eitt brot.

$$A=\frac{3000\times 1269734648531914468903714880493455422104626762401}{26973464853191446890371488049345542210462676240100}$$

Margfaldaðu 3000 og 1269734648531914468903714880493455422104626762401 til að fá út 3809203945595743406711144641480366266313880287203000.

$$A=\frac{3809203945595743406711144641480366266313880287203000}{26973464853191446890371488049345542210462676240100}$$

Minnka brotið \frac{3809203945595743406711144641480366266313880287203000}{26973464853191446890371488049345542210462676240100} eins mikið og hægt er með því að draga og stytta út 300.

$$A=\frac{12697346485319144689037148804934554221046267624010}{89911549510638156301238293497818474034875587467}$$

Úthluta A

$$A≔\frac{12697346485319144689037148804934554221046267624010}{89911549510638156301238293497818474034875587467}$$