Question

Evaluate the given series:
∑_n=9[infinity]21/n²+3

Answer 1

To evaluate the given series, rewrite it and use the formula for the sum of a geometric series.

Step-by-step explanation:

To evaluate the given series ∑_n=9[∞]21/n²+3, we can rewrite it as ∑_n=9[∞]2(n²+3).

Then, we can use the formula for the sum of a geometric series to simplify the expression.

The formula is: S = a / (1 - r), where S is the sum of the series, a is the first term, and r is the common ratio. In this case, a = 2(9²+3) and r = 1/n².

Plugging in the values, we get S = 2(9²+3) / (1 - (1/n²)).