onsider the infinite sum S = n=1 1 n2 . It is known that the value of this series is 2 6 . Using a computer, you find that the 99th partial sum of the series is equal to S99 = 99 n=1 1 n2 = 1.634883900... a. Draw pictures which illustrate the following inequalities: n=100 1 n2 100 dx x2 n=100 1 n2 99 dx x2 b. Using the inequalities above, the computed value of S99, and the known value of S, show that 3.14154 3.14165