Consider the series+ k=1 1 k(k + 1) = 1 1 2 + 1 2 3 + . (a) Show that 1 k 1 k + 1 = 1
Chapter 9, Problem 37(choose chapter or problem)
Consider the series+ k=1 1 k(k + 1) = 1 1 2 + 1 2 3 + . (a) Show that 1 k 1 k + 1 = 1 k(k + 1). (b) Use part (a) to find the partial sums S3, S10, and Sn. (c) Use part (b) to show that the sequence of partial sums Sn, and therefore the series, converges to 1.
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