$Prove that $1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}} \leq 2 \sqrt{n}-1$$

Question

Use induction to prove that
$$1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}} \leq 2 \sqrt{n}-1,$$
for all $n\geq 1$.

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Answer 1

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$Matchmaticians Prove that $1+\frac{1}{\sqrt{2}}+\dots+\frac{1}{\sqrt{n}} \leq 2 \sqrt{n}-1$ File #1$ File #1 (pdf)