Show that the series is convergent. How many terms of the series do we need to a

abondantQ

abondantQ

Answered question

2021-09-14

Show that the series is convergent. How many terms of the series do we need to add in order to find the sum to the indicated accuracy? summation n=1 to infinity (1)n+1n6 (|error|<0.00005)

Answer & Explanation

Willie

Willie

Skilled2021-09-15Added 95 answers

Step 1
Note that, {n=1}(1)n+1n6is a a alternating series.
Clearly an=1n6 is mjnjtjnically decreasing for all n>1
Therefore by alternating Series Test, the given series converges.
Also Remember that? the error of the nth partial sum is bounded by |an+1|
Therefore? we find the smallest n such that, a_{n}<0.00005
And we will conclude that, the sum jf first n-1 therms of the series approximate the sun within the allotted error.
The summation starts from n=1, therefore there are n-1 terms before an

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