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## Homework Statement

Find the formula of this serie knowing its first five terms:

[tex]1 +\left(\frac{2}{5}\right)^{2} +\left(\frac{3}{8}\right)^{3} +\left(\frac{4}{11}\right)^{4} +\left(\frac{5}{14}\right)^{5} + \cdots[/tex]

**2. Relevant formulas**

If the first term was 1/2 then the formula would simply be

[tex]\sum_{i = 1}^{\infty}\left(\frac{i}{2+3(i-1)}\right)^{i}[/tex]

but the first term being 1, I can't see how to do it...

(Maybe the first term IS 1/2 and it got missprinted in the book ?)

Also, the answer is not given in the book.

## The Attempt at a Solution

I've tried these as possible values for a first item equal to 1 without any success:

[tex]\left(\frac{1}{2}\right)^{0}=1[/tex]

[tex]\left(\frac{1}{1}\right)^{1}=1[/tex]

[tex]\left(\frac{2}{2}\right)^{1}=1[/tex]

So, is there a formula for this serie with first term = 1 ?

**Thanks !**