Hello,

The first step is to prove it is true for n=1.

The second step is to state the inductive hypothesis, that is to say assuming that

The third step is to prove that it is true if you "replace" n by n+1, that is to say :

Now, use the inductive hypothesis to substitute

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Another way would have been to note that and use telescoping series (Telescoping series - Wikipedia, the free encyclopedia)