Question

\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{99.101}\)=?

Answer 1

\(A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{99.101}\)

=\(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{99}-\frac{1}{101}\)

=\(\frac{1}{1}-\frac{1}{101}=\frac{101}{101}-\frac{1}{101}=\frac{100}{101}\)

Answer 2

=> A = 1 - 1 /3 + 1 /3 -1 /5 + 1/5 - 1 /7 +....+ 1/ 99 - 1/ 101

=> A = 1 - 1 /101

=> A =100/101

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