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1.

∞

Ʃ (1+n)/[(n)(2

n=1

2. When I see that there is an n as an exponent, I think to do the ratio test.

___________________________________________________________________________

[itex]\frac{\frac{1+n+1}{(n+1)(2^{n+1})}}{\frac{1+n}{(n)(2^{n})}}[/itex]

= [itex]\frac{n(n+2)}{2(n+1)^{2}}[/itex]

= [itex]\frac{n^{2} + 2n}{2(n+1)^{2}}[/itex]

Would equal ∞/∞, so I think I'm supposed to do L'Hospital's rule...

→L'Hospital's→ [itex]\frac{2n^{2} + 2}{4n + 2}[/itex]

I think it would still equal ∞/∞, so would I do L'Hospital rule again???

→L'Hospital's→ [itex]\frac{4n + 2}{4}[/itex]

It no longer equals ∞/∞, so would we then have: n + 1/2 = ∞

This really doesn't seem right... :/

Please help!

Thanks so much! :D

∞

Ʃ (1+n)/[(n)(2

^{n})]n=1

2. When I see that there is an n as an exponent, I think to do the ratio test.

___________________________________________________________________________

[itex]\frac{\frac{1+n+1}{(n+1)(2^{n+1})}}{\frac{1+n}{(n)(2^{n})}}[/itex]

= [itex]\frac{n(n+2)}{2(n+1)^{2}}[/itex]

= [itex]\frac{n^{2} + 2n}{2(n+1)^{2}}[/itex]

Would equal ∞/∞, so I think I'm supposed to do L'Hospital's rule...

→L'Hospital's→ [itex]\frac{2n^{2} + 2}{4n + 2}[/itex]

I think it would still equal ∞/∞, so would I do L'Hospital rule again???

→L'Hospital's→ [itex]\frac{4n + 2}{4}[/itex]

It no longer equals ∞/∞, so would we then have: n + 1/2 = ∞

This really doesn't seem right... :/

Please help!

Thanks so much! :D

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