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Using the induction method, show that if $n$ is an integer $>1$ then $1 + 1/2 + 1/3 +… + 1/n = 2/(n-1)$

Using the induction method, show that if $n$ is an integer $>1$ then
$$1 + frac{1}{2} + frac{1}{3} +… + frac{1}{n} = frac{2}{n-1}$$
I’m stuck in the proof, how would you solve this one?

A:

We will assume $n>2$. Let $f(x)=sum_{k=1}^n frac 1k = frac1n sum_{k=1}^n k = frac1n frac{n(n+1)}{2}$ (i.e. the sum of the first $n$ natural numbers) and we will check that $f(n+1)$ is equal to $frac 2{n+1}$
$$
f(n+1)=frac1{n+1}(n+1)(n+2) = frac{n+1}{n+1}n+1 cdot frac{n+2}{n+1}=
frac{n^2+3n+2}{n+1}=frac{2n+2}{n+1}=frac2{n+1}
$$
So the claim holds.

A:

You do induction, you prove the statement is true for a given $n$ and you show that the statement is true for $n+1$.
If $n=1$ then $2=1+frac{1}{2}=frac{2}{1 70238732e0

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