Question

The series 1/25+1/36+1/49+... is convergent..
True or Flase?

Answer 1

The series 1/25 + 1/36 + 1/49 + ... is convergent.

Step-by-step explanation:

The series 1/25 + 1/36 + 1/49 + ... is convergent. True.

To determine if a series is convergent or divergent, we need to check if the terms in the series approach zero as the index increases. In this series, the terms are getting smaller and approaching zero, so the series is convergent.

To see why the terms are getting smaller, let's look at the pattern:

1. The first term is 1/25, which is less than 1.
2. The second term is 1/36, which is less than 1/25.
3. The third term is 1/49, which is less than 1/36.

As the index increases, the denominator of each term is increasing, making the terms smaller. This shows that the series is convergent.