다음을 풀어보세요: 40div0.0585*(1-1.0585^-16+1000div1.0585^16

$$40 \div 0.0585 \times (1- { 1.0585 }^{ -16 } +1000 \div { 1.0585 }^{ 16 }$$

계산

$$\frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}\approx 275736.399448743$$

해답 단계

분자와 분모 모두에 10000을(를) 곱하여 \frac{40}{0.0585}을(를) 확장합니다.

$$\frac{400000}{585}\left(1-1.0585^{-16}+\frac{1000}{1.0585^{16}}\right)$$

5을(를) 추출 및 상쇄하여 분수 \frac{400000}{585}을(를) 기약 분수로 약분합니다.

$$\frac{80000}{117}\left(1-1.0585^{-16}+\frac{1000}{1.0585^{16}}\right)$$

1.0585의 -16제곱을 계산하여 \frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}을(를) 구합니다.

$$\frac{80000}{117}\left(1-\frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{1.0585^{16}}\right)$$

1에서 \frac{65536000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}을(를) 빼고 \frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}을(를) 구합니다.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{1.0585^{16}}\right)$$

1.0585의 16제곱을 계산하여 2.4834407193619933163914470962704442036969407810106396636962890625을(를) 구합니다.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{1000}{2.4834407193619933163914470962704442036969407810106396636962890625}\right)$$

분자와 분모 모두에 10000000000000000000000000000000000000000000000000000000000000000을(를) 곱하여 \frac{1000}{2.4834407193619933163914470962704442036969407810106396636962890625}을(를) 확장합니다.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{10000000000000000000000000000000000000000000000000000000000000000000}{24834407193619933163914470962704442036969407810106396636962890625}\right)$$

152587890625을(를) 추출 및 상쇄하여 분수 \frac{10000000000000000000000000000000000000000000000000000000000000000000}{24834407193619933163914470962704442036969407810106396636962890625}을(를) 기약 분수로 약분합니다.

$$\frac{80000}{117}\left(\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}+\frac{65536000000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}\right)$$

\frac{97218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}과(와) \frac{65536000000000000000000000000000000000000000000000000000}{162754770984107593983029876901179831333482711024313281}을(를) 더하여 \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}을(를) 구합니다.

$$\frac{80000}{117}\times \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}$$

\frac{80000}{117}과(와) \frac{65633218770984107593983029876901179831333482711024313281}{162754770984107593983029876901179831333482711024313281}을(를) 곱하여 \frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}(을)를 구합니다.

$$\frac{5250657501678728607518642390152094386506678616881945062480000}{19042308205140588496014495597438040266017477189844653877}$$