if myan = 1 / (n+1)^2

can i use p series test to confirm that the series will converge..

where p = 2..

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- Dec 9th 2009, 09:54 AMnameck[SOLVED] Series (p-series)
if my

**a**n = 1 / (n+1)^2

can i use p series test to confirm that the series will converge..

where p = 2.. - Dec 9th 2009, 10:18 AMosolage
no it wont work. the p series test only works when the denominator is n raised to a power 1/n or 1/n^2 or 1/n^(3/2)

even when you indirectly use the p series test with direct comparison or limit comparison an must still be in the form of 1/n

the integral test works the integral 1/(x+1)^2 ,x,0,infinity converges thus the series converges ... the sum however is not found that way. - Dec 9th 2009, 10:19 AMnameck
ok..so.. what test should i use to know whethere it is convergence or divergence?

- Dec 9th 2009, 10:31 AMPlato
Well of course it works. One just has to understand the process.

$\displaystyle \sum\limits_{n = 1}^\infty {\frac{1}{{\left( {n + 1} \right)^2 }}} = \sum\limits_{k = 2}^\infty {\frac{1}{{\left( k \right)^2 }}} $

The series on the right is a convergent p-series.

Of notice that $\displaystyle \frac{1}{(n+1)^2}\le \frac{1}{n^2}$ use comparison test. - Dec 9th 2009, 10:36 AMosolagepolar to cartesian
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