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Question

Tính A= 1+1/2+1/2^2+1/2^3+.....+1/2^100B= 1+1/3+1/3^2+1/3^3+...+1/3^100Giúp mk vs!!!!

Không Tên · Accepted Answer

$A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}$$\Rightarrow$$2A=2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{99}}$$\Rightarrow$$2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)$$\Rightarrow$$A=2-\frac{1}{2^{100}}$$B=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}$$\Rightarrow$$3B=3+1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^{99}}$$\Rightarrow$$3B-B=\left(3+1+\frac{1}{3}+...+\frac{1}{3^{99}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\right)$$\Rightarrow$$2B=3-\frac{1}{3^{100}}$$\Rightarrow$$B=\frac{3-\frac{1}{3^{100}}}{2}$Câu trả lời: $A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+....+\frac{1}{2^{100}}$$\Rightarrow$$2A=2+1+\frac{1}{2}+\frac{1}{2^2}+....+\frac{1}{2^{99}}$$\Rightarrow$$2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{99}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{100}}\right)$$\Rightarrow$$A=2-\frac{1}{2^{100}}$$B=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{100}}$$\Rightarrow$$3B=3+1+\frac{1}{3}+\frac{1}{3^2}+....+\frac{1}{3^{99}}$$\Rightarrow$$3B-B=\left(3+1+\frac{1}{3}+...+\frac{1}{3^{99}}\right)-\left(1+\frac{1}{3}+\frac{1}{3^2}+...+\frac{1}{3^{100}}\right)$$\Rightarrow$$2B=3-\frac{1}{3^{100}}$$\Rightarrow$$B=\frac{3-\frac{1}{3^{100}}}{2}$

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