1. ## Limit of series

Given Ur = 3/ (r2+3r)
I have simplified nr=1 Ur in terms of n by expressing in partial fraction.
Determine the value of r=1 Ur , deduce the value of r=2 U​r+1
I just don’t know how to deduce . Can anyone explain to me ?

2. ## Re: Limit of series

Originally Posted by Ahjiao
Determine the value of r=1 Ur , deduce the value of r=2 U​r+1
Decompose into partial fractions $\dfrac{3}{r^2+3r}=\dfrac{1}{r}-\dfrac{1}{r+3}$ and look here:

Convergence of the series 1 / n(n+2)

3. ## Re: Limit of series

If you know the value of $\sum_{r=1}^{\infty}U_r$, you should be able to find the value of $\sum_{r=3}^{\infty}U_r$. You just subtract the first two terms.

And this new sum is the same as $\sum_{r=2}^{\infty}U_{r+1}$. If you're having trouble seeing it, write the first few terms of each.

- Hollywood