- #1

ILoveBaseball

- 30

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Consider the series

[tex]\sum_{n=1}^\infty \frac{n}{\sqrt{5n^2+5}}[/tex]

Value ______

[tex]a_1 = .316227766, a_2 = 2/5, a_3 = .4242640687, a_4 = .4338609156[/tex]

there doesn't seem to be any common ratio, so that means that this isn't a geometric series right?

well i think i can simplify the equation to:

[tex]\frac{1}{\sqrt{5}}\sum_{n=1}^\infty \frac{n}{\sqrt{(n^2+1)}}[/tex]

hmm, that's as far as i got, can someone help me ?

[tex]\sum_{n=1}^\infty \frac{n}{\sqrt{5n^2+5}}[/tex]

Value ______

[tex]a_1 = .316227766, a_2 = 2/5, a_3 = .4242640687, a_4 = .4338609156[/tex]

there doesn't seem to be any common ratio, so that means that this isn't a geometric series right?

well i think i can simplify the equation to:

[tex]\frac{1}{\sqrt{5}}\sum_{n=1}^\infty \frac{n}{\sqrt{(n^2+1)}}[/tex]

hmm, that's as far as i got, can someone help me ?

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