Question

Cho A = \(\frac{1}{1.2}+\frac{1}{3.4}+...+\frac{1}{49.50}\)

CMR: A = \(\frac{1}{26}+\frac{1}{27}+\frac{1}{28}+...+\frac{1}{49}+\frac{1}{50}\)

Answer 1

\(A=\frac{1}{1}-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{49}-\frac{1}{50}\)

A = \(\left(\frac{1}{1}+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{49}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)

A = \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{49}+\frac{1}{50}\right)-2.\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{50}\right)\)

A = \(\left(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+...+\frac{1}{49}+\frac{1}{50}\right)-\left(\frac{1}{1}+\frac{1}{2}+...+\frac{1}{25}\right)\)

A = \(\frac{1}{26}+\frac{1}{27}+...+\frac{1}{49}+\frac{1}{50}\)

Answer 2

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