Let where
Prove that the sequence converges.
Hint: Show, first, that for any . Then show that the sequence increases and . Use the theorem about the convergence and divergence of p-series to complete the proof.
How should I proceed?
Let where
Prove that the sequence converges.
Hint: Show, first, that for any . Then show that the sequence increases and . Use the theorem about the convergence and divergence of p-series to complete the proof.
How should I proceed?
Hey vidomagru.
If you can show that the difference is < 1/(2(n+1))^2 then the ratio test should be sufficient to show convergence of the sequence.
Think of a power series and how the ratio test is used to show convergence (in terms of an+1/an where an is the nth coefficient).
The other hint: Use the x > ln(1+x) to bound the difference that takes into account the logarithm term (i.e. ln(1+x) - ln(x) < x+1-x = 1).