calo2ndro8Knillis calo2ndro8Knillis

21-11-2016
Mathematics

Answered

Determine whether the sequence:

ln(2n^2 +1) - ln(n^2 +1)

converges or diverges. If the sequence converges, find the limit.

Verified Answer :

alsteva alsteva

22-11-2016

\(\\ \lim_{n \to \infty} \ln{ (2n^2+1) }-\ln{(n^2+1)} \\ \\ \lim_{n \to \infty} \ln{ \frac{2n^2+1}{n^2+1} } \\ \\ \lim_{n \to \infty} \ln{ \frac{ \frac{2n^2}{n^2} + \frac{1}{n^2}}{ \frac{n^2}{n^2}+ \frac{1}{n^2}} } \\ \\ \lim_{n \to \infty} \ln{ \frac{ 2 + \frac{1}{n^2}}{ 1+ \frac{1}{n^2}} } \\ \\ \ln{ \frac{ 2 + 0}{ 1+ 0} } \\ \\ \ln{2}\)

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