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## Homework Statement

Prove that H

_{1}+H

_{2}+...+H

_{n}= (n +1)(H

_{n}-n)?

## Homework Equations

H

_{n}denotes the nth harmonic number.

The nth harmonic number is the sum of 1+1/2+...1/n,

which is n / n +1.

I'm not really sure if H

_{n}= (1/ n) .

Prove by Mathematical Induction

H

_{n}denotes the nth harmonic number.

## The Attempt at a Solution

Basis Step : P(1) = H

_{n}= (n +1)(H

_{n}-n)

(1 / n) = (n +1) ( (1 / n) -n)

(1) = ( 1 + 1) (1-1)

1 = (2) (0)

1 = 0, which is false

or

Basis Step:

P(1) = Hn = H

_{n}= (n +1)(H

_{n}-n)

( n / n + 1) = (n + 1) ( (n / n + 1) -1)

P(1) is false, because 1/ 2 does not equal to - 1