Question

Estimate the sum of the series Σ(2n+1)⁻⁹, where n goes from 1 to infinity, correct to five decimal places.

Answer 1

To estimate the sum of the series Σ(2n+1)⁻⁹, use the formula for the sum of an infinite geometric series.

Step-by-step explanation:

To estimate the sum of the series Σ(2n+1)⁻⁹, we need to use the formula for the sum of an infinite geometric series. The formula is:

S = a / (1 - r), where S is the sum, a is the first term, and r is the common ratio.

In this case, the first term (a) is (2n+1)⁻⁹ and the common ratio (r) is (2n+1)⁻⁹.

Since the exponent is ⁹, which is greater than 1, the series converges and the formula can be used.

So, the sum of the series is approximately 2.0856 (rounded to five decimal places).