Question

Calculate [(3²+1)/(3²-1)]+[(5²+1)/(5²-1)]+....+[(99²+1)/(99²-1)]

Answer 1

9+1/9-1+25+1/25-1+99+1/99-1 10/8+26/24+100/98 1.25+1.08+1.02 2.33+1.02 3.35

Answer 2

Every term of series simplifies to $1 + \frac{1}{(x - 1)} - \frac{1}{(x + 1)}$ and x = 3, 5, 7, ...., 99 (odd numbers).

Now write first three or four terms of series, each in new line, by putting x = 3, 5, 7, 9. You can see that some terms will be cancelled out.

The final sum is given by $49 + \frac{1}{2} - \frac{1}{100}$, it simplifies to $\frac{4949}{100}$

Answer = $\frac{4949}{100}$