Question

Bài 1 : Tính nhanh các tổng sau : 

a) S = \(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+........+\frac{2}{2017x2019}\)

b A = \(\frac{1}{3}+\frac{1}{9}+\frac{1}{27}+\frac{1}{81}+..........+\frac{1}{729}+\frac{1}{2187}\)

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Answer 1

Câu a

\(S=\frac{3-1}{1x3}+\frac{5-3}{3x5}+\frac{7-5}{5x7}+...+\frac{2019-2017}{2017x2019}.\)

\(S=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{2017}-\frac{1}{2019}=1-\frac{1}{2019}=\frac{2018}{2019}\)

Câu b

\(A=\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\frac{1}{3^4}+...+\frac{1}{3^6}+\frac{1}{3^7}\)

\(3A=1+\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+...+\frac{1}{3^5}+\frac{1}{3^6}\)

\(2A=3A-A=1-\frac{1}{3^7}\Rightarrow A=\frac{1}{2}-\frac{1}{2.3^7}\)