Question

The infinite sum $1 + \frac{4}{7} + \frac{9}{72} + \frac{16}{73} + \frac{25}{74} + \dots$ equals:

• A. 27
• B. 21
• C. 49
• D. 256

Hint:

When dealing with infinite sums, break down the series into recognizable forms or use standard sum formulas.

Answer 1

The Correct Option is C

We can write the given sum as: \[ S = \sum_{n=1}^{\infty} \frac{n^2}{(n+6)} \] Using the properties of infinite sums and manipulating the terms, we find that the sum converges to 49.