Consider the series ∑n=1∞(−1)nn2. Evaluate the the following limit.?
回答 (2)
2020-08-19 9:28 pm
a_(n+1) = (-1)^(n+1)/(n+1)² and an = (-1)ⁿ/n².
Their ratio and simplifying [highschool algebra] gives -1*(n/(n+1))².
Your limit requires the absolute value of this, hence you simply have (n/(n+1))².
Whats the limit of that? Or, recall that this can be written as
( 1/(1 + 1/n) )². If n ~ ∞, what does it give? You have your answer!
Their ratio and simplifying [highschool algebra] gives -1*(n/(n+1))².
Your limit requires the absolute value of this, hence you simply have (n/(n+1))².
Whats the limit of that? Or, recall that this can be written as
( 1/(1 + 1/n) )². If n ~ ∞, what does it give? You have your answer!
收錄日期: 2021-04-24 07:56:40
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