Sequence and series

Question

find the sum of the following series: S = 7/6 + 13/12 + 21/20 +31/30 +............. + 9901/9900

A) 9749/100

B) 9849/100

C) 9949/100

D) 9649/100

Answer 1

The terms are a_n = (n²+3n+3)/(n²+3n+2) for n=1,2,3.....

The sequence a_n converges to 1; therefore, the infinite series cannot converge!

A finite number of terms certainly has a sum, but not infinitely many.