Question

Evaluate: (3²+1)/(3²-1)+(5²+1)/(5²-1)+.... +(99²+1)/(99²-1)

Answer 1

Answer:

Every term of series simplifies to  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 , it simplifies to