Despite its wide range of styles and instrumentation, country music has certain common features _____ its own special character.

A. give it that 

B. give which

C. that gives it to

D. that give it

Nhân 3 vào ba vế của A , ta được :

\(3A=3.\left(\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+....+\frac{1}{3^{99}}+\frac{1}{3^{100}}\right)\)

\(\Rightarrow3A=1+\frac{1}{3^1}+\frac{1}{3^2}+....+\frac{1}{3^{98}}+\frac{1}{3^{99}}\)

Lấy biểu thức 3A - A , ta được :

\(3A-A=\left(1+\frac{1}{3^1}+\frac{1}{3^2}+....+\frac{1}{3^{98}}+\frac{1}{3^{99}}\right)-\left(\frac{1}{3^1}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^{99}}+\frac{1}{3^{100}}\right)\)

\(\Rightarrow2A=1-\frac{1}{3^{100}}\)

\(\Rightarrow A=\left(1-\frac{1}{3^{100}}\right):2\)

Ta xét : \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{19}-\frac{1}{20}=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{19}\right)-\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{20}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+....+\frac{1}{20}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{20}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{9}+\frac{1}{10}\right)\)

\(=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\)

Vì \(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+...+\frac{1}{20}\)

nên \(1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{19}-\frac{1}{20}=\frac{1}{11}+\frac{1}{12}+\frac{1}{13}+....+\frac{1}{20}\) ( đpcm )

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