somatorios

por LUCINEIA ROCHA Dom 01 Mar 2015, 15:51

somatorios

por LUCINEIA ROCHA Dom 01 Mar 2015, 15:51

por **Carlos Adir** Dom 01 Mar 2015, 16:15

Re: somatorios

por Carlos Adir Dom 01 Mar 2015, 16:15

$\\ \sum_{i=1}^n\left(\dfrac{i+1}{2i-1}-\dfrac{i+2}{2i+1} \right )=\sum_{i=1}^n \left(\dfrac{(i+1)(2i+1)-(i+2)(2i-1)}{(2i-1)(2i+1)} \right )= \\ =\sum_{i=1}^{n}\left(\dfrac{2i^2+3i+1-2i^2-3i+2}{4i^2-1} \right )=\sum_{i=1}^n \left(\dfrac{3}{4i^2-1} \right )=\dfrac{3n}{2n+1}$

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