Question

3/1x3+3/3x5 x3/5x7+........+3/97x99+3/99x101

Answer 1

A = \(\frac{3}{1\times3}\) + \(\frac{3}{3\times5}\) + ... + \(\frac{3}{97\times99}\) + \(\frac{3}{99\times101}\)

A = \(\frac32\) x (\(\frac{2}{1\times3}\) + \(\frac{2}{3\times5}\) + ... + \(\frac{3}{99\times101}\))

A = \(\frac32\) x (\(\frac11\) - \(\frac13\) + .. + \(\frac{1}{99}\) - \(\frac{1}{99}-\frac{1}{101}\))

A = \(\frac32\) x (\(\frac11\) - \(\frac{1}{101}\))

A = \(\frac32\) x \(\frac{100}{101}\)

A = \(\frac{150}{101}\)