Question

Evaluate the series or state that it diverges.
∑_k=2^[infinity](1/4)⁴ k

Answer 1

The given series converges to 1/15.

Step-by-step explanation:

The given series can be written as:

∑k=2∞(1/4)4k

Using the formula for the sum of a geometric series, where a is the first term and r is the common ratio, we have:

∑k=2∞(1/4)4k = a / (1 - r)

Since the common ratio r = (1/4)4, which is less than 1, the series converges. Evaluating the series gives:

a / (1 - r) = (1/16) / (1 - (1/256)) = 1/15