\(A=\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{99.101}=>2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-...-\frac{1}{101}\)
A= 1/2(1/3 - 1/101)
A= 49/303
1/5 + 1/35 + 1/63 + 1/99 + ..... + 1/9999
= 1/3x5 + 1/5x7 + 1/7x9 + 1/9x11 + .....+ 1/99x101
= 1/3 - 1/101
= 98/303
= 98/303 : 2
= 98/606
= 49/303
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