Use the Root Test to determine the convergence or divergence of the series. $$\sum _ { n = 1 } ^ { \infty } \left( \frac { 7 n ^ { 2 } + 1 } { 10 n ^ { 2 } - 1 } \right) ^ { n }$$
A) Root Test inconclusive
B) converges
C) diverges

Question

Quizplus · Accepted Answer

The limit of the nth root of the nth term is 1/10, which is less than 1. So the series converges by the Root Test.

Use the Root Test to Determine the Convergence or Divergence ∑n=1∞(7n2+110n2−1)n\sum _ { n = 1 } ^ { \infty } \left( \frac { 7 n ^ { 2 } + 1 } { 10 n ^ { 2 } - 1 } \right) ^ { n }n=1∑∞​(10n2−17n2+1​)n

Use the Root Test to Determine the Convergence or Divergence $\sum _ { n = 1 } ^ { \infty } \left( \frac { 7 n ^ { 2 } + 1 } { 10 n ^ { 2 } - 1 } \right) ^ { n }$