Question

If $1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+...=\frac{\pi }{4}$, then value of $\frac{1}{1.3}+\frac{1}{5.7}+\frac{1}{9.11}+...=$

• A. $\frac{\pi }{8}$
• B. $\frac{\pi }{6}$
• C. $\frac{\pi }{4}$
• D. $\frac{\pi }{36}$

Answer 1

The correct option is A $\frac{\pi }{8}$

$s=\pi /4$

$\frac{1}{1.3}+\frac{1}{5.7}+\frac{1}{9.11}+.....=\frac{1}{2}(1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...)$

Required sum$=1/2\ast [1-1/3+1/5-1/\mathrm{7......}]=1/2\ast s=\pi /8$