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

answer: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.

step-by-step explanation: if you weigh 60 pounds on earth, on the moon you will weigh about 10 pounds. if you weigh 120 pounds on earth, you will weigh about 20 pounds on the moon. since weight is caused by the mass of two objects that are near each other, the bigger the objects, the more the force of gravity.