Question

Use the ratio test to determine whether ∑ₙ=26[infinity]n(-4)ⁿ/n. converges or diverges.

Answer 1

To determine whether the series ∑ₙ=26ⁿ[infinity]ₙ(-4)ⁿ/ₙ converges or diverges, apply the ratio test and find that the series diverges.

Step-by-step explanation:

To determine whether the series ∑n=26∞ (n(-4)n/n) converges or diverges, we can use the ratio test. The ratio test states that if ∑an converges, then the limit of the absolute value of (an+1/an) as n approaches infinity is less than 1.

Let's apply the ratio test to the given series:

limn→∞ |(n+1)(-4)n+1/(n+1)| / (n(-4)n/n)

= limn→∞ |-4(n+1)/n|

= limn→∞ |4(n+1)/n|

= 4

Since the limit is 4, which is greater than 1, the series diverges.