Câu hỏi của Tuananh Vu

Question

Rút Gọn:

B=1+1/2+1/2^2+1/2^3+...+1/2^250

Isolde Moria · Accepted Answer

Ta có

$B=1+\frac{1}{2}+.....+\frac{1}{2^{250}}$

$\Rightarrow2B=2+1+....+\frac{1}{2^{251}}$

$\Rightarrow2B-B=\left(2+1+....+\frac{1}{2^{251}}\right)-\left(1+\frac{1}{2}+.....+\frac{1}{2^{250}}\right)$

$\Rightarrow B=2-\frac{1}{2^{251}}$

Câu trả lời:

Ta có

$B=1+\frac{1}{2}+.....+\frac{1}{2^{250}}$

$\Rightarrow2B=2+1+....+\frac{1}{2^{251}}$

$\Rightarrow2B-B=\left(2+1+....+\frac{1}{2^{251}}\right)-\left(1+\frac{1}{2}+.....+\frac{1}{2^{250}}\right)$

$\Rightarrow B=2-\frac{1}{2^{251}}$