N 3. Let SN = ) n4 In this problem, you will see how to slightly modify SN to generate a much more accurate n=1 00 approximation to n=1 a) Compute 34. b) Find an upper bound on the error when using S, to approximate S..and call it UA. Find a lower bound on the error when using S, to approximate S.. and call it L4. () Compute L4 + S4, U4 + $4, and explain why b, | S, - S. could be . g) Compute an upper bound on the magnitude of the error if you use ( LA + 54 ) + (U4 + 54 ) 2 instead of S4 to approximate Soo. Compare this to the original upper bound U4 h) Just using fact that RN dx, find the smallest N to guarantee that SN approximates S. to eight decimal places. 1) Using the ideas above, and the fact that edx