Lim n-cos- - n 2 -n - -n- Z is equal to

The correct option is A 0 n+∞ #160; lim #160; cos [π√( n ^ 2 +n)] = n+∞ #160; lim #160; cos #160;( π n( 1+ 1 / n #160; ) ^ 1 / ...

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Byju's Answer

Standard XII

Mathematics

Chain Rule of Differentiation

lim n→∞cos[ π...

Question

$lim n \to \infty cos [π \sqrt{n^{2} + n}], n \in Z$ is equal to

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Solution

The correct option is A $0$
$l i m n + \infty c o s [π \sqrt{n^{2} + n}]$

$= l i m n + \infty c o s (π n {(1 + \frac{1}{n})}^{\frac{1}{2}})$

$= l i m n + \infty c o s (π n (1 + \frac{1}{2 n}))$

$= l i m n + \infty c o s (n π + \frac{π}{2})$

$= l i m n + \infty s i n n π$

$= l i m n + \infty 0$

$= 0$

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limn→∞cos[π√n2+n],n∈Z is equal to

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