Test the series for convergence or divergence. \sum_{n=0}^\infty\frac{(-1

Lipossig

Lipossig

Answered question

2021-10-24

Test the series for convergence or divergence.
n=0(1)n+1n+4

Answer & Explanation

Raheem Donnelly

Raheem Donnelly

Skilled2021-10-25Added 75 answers

Given:
n=0(1)n+1n+4
On applying radical rule
n=0(1)n+1n+4=n=0(1)n+1(n+4)12
On applying rule exponent rule
n=0(1)n+1n+4=n=0(1)n+1(n+4)12
On simplifying,
(n+4)12=1n+4
n=0(1)n+1n+4=n=0(1)n+11n+4
On applying the alternating series test the function converges
therefore, n=0(1)n+1n+4 converges

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