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Q30E

Expert-verifiedFound in: Page 330

Book edition
7th

Author(s)
Kenneth H. Rosen

Pages
808 pages

ISBN
9780073383095

Prove that ${H}_{1}+{H}_{2}+\dots +{H}_{n}=(n+1){H}_{n}-n$

${H}_{{2}^{\mathrm{\prime}}}\le 1+n$ is a non negative integer.

If ${H}_{1}=1$

it is true for n=1.

Let P(k) be true.

${H}_{1}+{H}_{2}+\dots +{H}_{k}=(k+1){H}_{k}-k$

We need to prove that P(k+1) is true.

$\begin{array}{r}{H}_{1}+{H}_{2}+\dots +{H}_{k}\\ (k+1){H}_{k}-k+{H}_{k+1}\\ =(k+1){H}_{k}-k\end{array}$

It is true for P (k+1) is true

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