00:01
So everyone, we need to determine whether the given series summation n equal to 1 to infinity n by 3 power n is convergent or divergence using the ratio test.
00:13
First, let us write a n from the given series.
00:18
A .n is nothing but n by 3 power n.
00:22
From this we can also write a .n plus 1, which is nothing but we replace n by n plus 1, that is n plus 1.
00:31
1 by 3 power n plus 1.
00:34
So now let us recall the definition of the ratio test.
00:40
So in ratio test, if l is equal to limit n tends to infinity, modulus of an plus 1 by a .n.
00:53
Then if l is less than 1, we have the series.
01:00
A .n.
01:08
Converges absolutely.
01:15
Also, if l is greater than 1, the series an diverges.
01:27
Whereas if l is equal to 1, then the test is inconclusive.
01:37
So using this, let us find whether the given series is convergent or divergent...