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Question
Evaluate the following:
`lim_(x->∞) (sum "n")/"n"^2`
Solution
`lim_(x->∞) (sum "n")/"n"^2`
= `lim_(x->∞) (("n"("n"+1))/2)/"n"^2`
= `lim_(x->∞) ("n"^2(1 + 1/"n"))/(2"n"^2)`
= `lim_(x->∞) 1/2(1 + 1/"n")`
= `1/2 (1+1/∞)`
`= 1/2`(1 + 0)
`= 1/2`
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