sum fof series?

**a69356** · Aug 20th 2009, 06:23 AM

How do we find the sum of the below series:
a)
1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
b)
1/2 + 1/6 + 1/12 + 1/20 + ......

Thanks!!!

**skeeter** · Aug 20th 2009, 06:45 AM

Originally Posted by a69356

How do we find the sum of the below series:
a)
1 + 1/3 + 1/6 + 1/10 + 1/15 + .........
b)
1/2 + 1/6 + 1/12 + 1/20 + ......

Thanks!!!

(b) $\sum_{n=1}^{\infty} \frac{1}{n(n+1)} = \sum_{n=1}^{\infty} \frac{1}{n} - \frac{1}{n+1} =$

$\left(1 - \frac{1}{2}\right) + \left(\frac{1}{2} - \frac{1}{3}\right) + ... + \left(\frac{1}{n-1} - \frac{1}{n}\right) + \left(\frac{1}{n} - \frac{1}{n+1}\right) + ... =$

$\lim_{n \to \infty} 1 - \frac{1}{n+1} = 1$

the series in (a) is just twice the sum of (b).

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