1. Prove by induction that $1 + \dots + \frac{1}{n^2} < 2$ for every positive integer $n$.
Added by Jerry B.
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Inductive step: Assume that 1 + In < 2 for some positive integer k. We want to show that 1 + Ik+1 < 2. Starting with 1 + Ik+1, we can rewrite it as 1 + Ik + 1. Since we know that 1 + Ik < 2 (by the induction hypothesis), we can substitute this in to get: 1 + Ik Show more…
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