Approximate the sum of the series by using the first six terms. (See Example 4. Round your answer to four decimal places.) [infinity] (−1)n + 1n 2n n = 1

0.1875

Step-by-step explanation:

The well formatted expression for the series has been attached to this response.

Each term in the series is govern by the rule, Tₙ

Where

n = term position

Tₙ =

To get the first six terms, we substitute n = 1 through 6 into Tₙ as follows:

When n = 1, we have;

T₁ = = 0.50000

When n = 2, we have;

T₂ = = -0.50000

When n = 3, we have;

T₃ = = 0.37500

When n = 4, we have;

T₄ = = -0.25000

When n = 5, we have;

T₅ = = 0.15625

When n = 6, we have;

T₆ = = -0.09375

Therefore, the approximate sum of the series using the sum of the first six terms is

=> T₁ + T₂ + T₃ + T₄ + T₅ + T₆

=> 0.50000 + -0.50000 + 0.37500 + -0.25000 + 0.15625 + -0.09375

=> 0.1875