Letxn:= 1/12 + 1/22 +... + I/n2 for each n eN. Prove that (xn) is increasing and
Chapter 3, Problem 12(choose chapter or problem)
Letxn:= 1/12 + 1/22 +... + I/n2 for each n eN. Prove that (xn) is increasing and bounded, and hence converges. [Hint:Note that if k ::: 2, then 1/ k2 ::: 1/ k(k - 1) = I/(k - 1) - 1/ k.] for n e N.
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