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# Sum of reciprocal sequence

Let be a sequence such that and

Evaluate the sum

Solution

Let us consider the sequence

and observe that

This in return means,

Thus,

which is the desired result. Therefore,

Notes:

1. The recursive relation has a closed form if-f or . In our case it is:

where .

2. The number is known as the Grafting constant.
3. Under the same assumptions it holds that