This works becasue 1 n 1 n 1 2 1 2 21 n1 n1 n n

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Unformatted text preview: = −1 to see that B = −1. This works becasue −1 n + 1 − (n − 1) 2 1 + = =2 . 2−1 n−1 n+1 n n −1 (a) We see that M sM = 1 2−1 − ···+ = = 1 1 + 1 2+1 1 3−1 + 1 (M −2)−1 1 1 − ···+ 1 2 M 2 1 1 = = − 2−1 n n−1 n+1 n=2 n=2 − 1 3 1 3+1 + 1 4−1 1 (M −2)+1 + 1 (M −1)−1 + 1 M −3 + ···+ − 1 2 1 1 + 3−1 4 5 1 1 M −1 + M −2 − − + + − 1 4+1 + − + 1 5−1 − 1 (M −1)+1 1 4 1 M − 1 6 + − + − + 1 M −1 1 M +1 − = (b) The sum of the series is 3 3 1 1 . − − = M →∞ 2 M M +1 2 lim sM = lim M →∞ 1 1 5+1 +... 1 M −1 − 1 M +1 +... +... 1 M − 1 M +1 1 1 3 − − . 2M M +1...
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