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The value of lim(x to oo) (1 + 2 + 3 …...

The value of `lim_(x to oo) (1 + 2 + 3 … + n)/(n^(2))` is

A

1

B

`(1)/(2)`

C

0

D

`(3)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
`underset(n to oo) ("lim") ( 1 + 2 + 3+… +n)/(n^(2)) = underset(n to oo) ("lim") (n(n + 1))/(2n^(2))`
`= underset(n to oo) ("lim")((1 + (1)/(n)))/(2) = (1)/(2)`
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