Consider the infinite series
k=1∑∞k2+11.
Let Sn denote the n-th partial sum and Rn the remainder k=n+1∑∞1/(k2+1).
(a) Justify that the series converges.
(b) Determine the least integer n such that Rn<0.01. Show all work that leads to your answer.
(c) Using the value of n found in part (b), state an interval of length less than 0.01 that contains the exact value of the series.