Determine whether those series are converge and diverge?if possible, find the limit of the convergent series.

1. ∑ (n^+2^n)/(n+3^n) from n=1 to infinite

2. log(8n^2 + 1) + 2 log(1/n)

3. [√(n^4+ 3n^2+ 1)] - n^2 -1 ( just this sequence, not "sum")

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- Nov 15th 2008, 04:04 AMJojo123Converge of Diverge
Determine whether those series are converge and diverge?if possible, find the limit of the convergent series.

1. ∑ (n^+2^n)/(n+3^n) from n=1 to infinite

2. log(8n^2 + 1) + 2 log(1/n)

3. [√(n^4+ 3n^2+ 1)] - n^2 -1 ( just this sequence, not "sum")

- Nov 15th 2008, 05:36 AMSoroban
Hello, Jojo123!

Quote:

We have: /

. . . . . .

Hence: .

. . . . . .

. . . . . .

This product has an infinite number of factors which are greater than 8.

. . Hence, the product diverges.

Therefore, the series diverges.

- Nov 15th 2008, 09:36 AMMathstud28
- Nov 15th 2008, 10:00 AMMoo
- Nov 15th 2008, 10:03 AMMathstud28