Question

Approximate

Σ (-1)⁽ⁿ⁺²⁾n! n=1
Use |S – Sn | = b₍ₙ₊₁₎
(Use decimal notation.
Give your answer to four decimal places.) S = _____ .

Answer 1

The given series Σ (-1)⁽ⁿ⁺²⁾n! n=1 does not converge to a specific value.

Step-by-step explanation:

The given series is Σ (-1)⁽ⁿ⁺²⁾n! n=1

To find the value of the series, we need to substitute different values of n and calculate the terms of the series.
For n = 1: (-1)⁽¹⁺²⁾1! = (-1)³ = -1
For n = 2: (-1)⁽²⁺²⁾2! = (-1)⁴2! = 2
For n = 3: (-1)⁽³⁺²⁾3! = (-1)⁵3! = -6

Continuing this pattern, we can observe that the series follows (-1)ⁿ⁺²⁾n! = -1, 2, -6, 24, ...

The terms alternate between -1 and 2 and increase in magnitude with every term. Therefore, the series does not converge to a specific value.