Câu hỏi của Trần Thu Giang

Question

Tính tồng

A=1/2+(1/2)²+(1/2)³+…+(1/2)²⁵

Nguyễn Lê Phước Thịnh · Accepted Answer

Ta có: $A=\frac12+\left(\frac12\right)^2+\left(\frac12\right)^3+\cdots+\left(\frac12\right)^{25}$

$=\frac12+\frac{1}{2^2}+\frac{1}{2^3}+\cdots+\frac{1}{2^{25}}$

=>$2A=1+\frac12+\cdots+\frac{1}{2^{24}}$

=>$2A-A=1+\frac12+\cdots+\frac{1}{2^{24}}-\frac12-\frac{1}{2^2}-\cdots-\frac{1}{2^{25}}$

=>$A=1-\frac{1}{2^{25}}=\frac{2^{25}-1}{2^{25}}$

Câu trả lời:

Ta có: $A=\frac12+\left(\frac12\right)^2+\left(\frac12\right)^3+\cdots+\left(\frac12\right)^{25}$

$=\frac12+\frac{1}{2^2}+\frac{1}{2^3}+\cdots+\frac{1}{2^{25}}$

=>$2A=1+\frac12+\cdots+\frac{1}{2^{24}}$

=>$2A-A=1+\frac12+\cdots+\frac{1}{2^{24}}-\frac12-\frac{1}{2^2}-\cdots-\frac{1}{2^{25}}$

=>$A=1-\frac{1}{2^{25}}=\frac{2^{25}-1}{2^{25}}$

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