Question

2/1x3 + 2/3x5 + 2/5x7 + ...+ 2/59x61

Answer 1

\(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+....+\frac{2}{59x61}\)

\(=\frac{2}{2}x\left(\frac{2}{1x3}+\frac{2}{3x5}+\frac{2}{5x7}+.....+\frac{2}{59x61}\right)\)

\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{59}-\frac{1}{61}\)

\(=1-\frac{1}{61}=\frac{60}{61}\)