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## Homework Statement

Let

[tex]P(x) = \displaystyle\sum\limits_{k=1}^\infty arctan (\frac{x-1}{(k+x+1)sqrt(k+1) + (k+2)sqrt(k+x)})[/tex] (infite sum from K=1 to infinity)

a) Simplify the expression for P(n), where n is a non-negative integer

## Homework Equations

[tex]tg(a-b)=\frac{tg(a)-tg(b)}{1+tg(a)tg(b)}[/tex]

## The Attempt at a Solution

Im looking for a hint. My first idea was to somehow use trig formulae, but i can't factorize the denominator or split it into partial fractions. Now im stuck, any hints?