Use the nth term test to investigate the series $\sum_{n=1}^{\infty} \frac{n+1}{n+2}$.
A) The series converges.
B) $\lim _{\mathrm{n} \rightarrow} \frac{\mathrm{n}+1}{\mathrm{n}+2}=1 \neq 0$, so the series diverges.
C) $\lim _{\mathrm{n} \rightarrow} \frac{\mathrm{n}+1}{\mathrm{n}+2}=0$, so the test fails to tell us anything about the series.
D) $\lim _{\mathrm{n} \rightarrow} \frac{\mathrm{n}+1}{\mathrm{n}+2}=1$, so the test fails to tell us anything about the series.

Question

Quizplus · Accepted Answer

The Answer is B

Use the Nth Term Test to Investigate the Series ∑n=1∞n+1n+2\sum_{n=1}^{\infty} \frac{n+1}{n+2}∑n=1∞​n+2n+1​

Use the Nth Term Test to Investigate the Series $\sum_{n=1}^{\infty} \frac{n+1}{n+2}$