Tính nhanh 1/2 +1/4+1/8+1/6+….+1/512+1/1024 07/11/2021 Bởi Amara Tính nhanh 1/2 +1/4+1/8+1/6+….+1/512+1/1024
Ta đặt A A=1/2+1/4+1/8+1/16+….+1/512+1/1024 A×2=(1/2+1/4+1/8+1/16+…..+1/512+1/1024) A×2=1+1/2+1/4+1/8+….+1/256+1/512 A×2-A=1+1/2+1/4+1/8+….+1/256+1/512-(1/2+1/4+1/8+1/16+….+1/512+1/1024) A=1-1/1024 A=1023/1024 Chúc bn học tốt Bình luận
Đáp án: A = $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + … + $\frac{1}{512}$ + $\frac{1}{1024}$ A = $\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$ $\frac{1}{2}$ . A = $\frac{1}{2}$ . ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$) $\frac{1}{2}$ . A = $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + … + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$ A – $\frac{1}{2}$ . A = ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$) – ($\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + … + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$) $\frac{1}{2}$ . A = $\frac{1}{2^{1}}$ – $\frac{1}{2^{11}}$ A = ($\frac{1}{2}$ – $\frac{1}{2048}$) . 2 A = $\frac{1023}{1024}$. Chúc học tốt!!! Bình luận
Ta đặt A
A=1/2+1/4+1/8+1/16+….+1/512+1/1024
A×2=(1/2+1/4+1/8+1/16+…..+1/512+1/1024)
A×2=1+1/2+1/4+1/8+….+1/256+1/512
A×2-A=1+1/2+1/4+1/8+….+1/256+1/512-(1/2+1/4+1/8+1/16+….+1/512+1/1024)
A=1-1/1024
A=1023/1024
Chúc bn học tốt
Đáp án:
A = $\frac{1}{2}$ + $\frac{1}{4}$ + $\frac{1}{8}$ + … + $\frac{1}{512}$ + $\frac{1}{1024}$
A = $\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$
$\frac{1}{2}$ . A = $\frac{1}{2}$ . ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$)
$\frac{1}{2}$ . A = $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + … + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$
A – $\frac{1}{2}$ . A = ($\frac{1}{2^{1}}$ + $\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + … + $\frac{1}{2^{9}}$ + $\frac{1}{2^{10}}$) – ($\frac{1}{2^{2}}$ + $\frac{1}{2^{3}}$ + $\frac{1}{2^{4}}$ + … + $\frac{1}{2^{10}}$ + $\frac{1}{2^{11}}$)
$\frac{1}{2}$ . A = $\frac{1}{2^{1}}$ – $\frac{1}{2^{11}}$
A = ($\frac{1}{2}$ – $\frac{1}{2048}$) . 2
A = $\frac{1023}{1024}$.
Chúc học tốt!!!