Evaluate the series sum_(n=2)^4 (-1)^n *((n+1)!)/(2n-2)?

Jon Wilkinson

Jon Wilkinson

Answered question

2023-01-14

Evaluate the series n=24(1)n(n+1)!2n2?

Answer & Explanation

Digngoorpr43

Digngoorpr43

Beginner2023-01-15Added 14 answers

Remember that
n=1kan=a1+a2++ak.
In other words, a series an is the partial sum of the sequence an.
In our case, the series begins with n=2 and ends with k=4.
an=(1)n(n+1)!2n2
Therefore,
n=24(1)n(n+1)!2n2=(1)23!2+(1)34!4+(1)45!6=36+20=17

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