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Mathematics Question on Limits

lim⁡x→∞\lim_{x\rightarrow \infty}{x−(x−a1)(x−a2)......(x−an)nx-\sqrt[n]{(x-a_1)(x-a_2)......(x-a_n)}} where a1,a2,.....an are positive rational numbers.The limit

A

does not exist

B

is a1+a2+....+ann\frac{a_1+a_2+....+a_n}{n}

C

is a1a2.....ann\sqrt[n]{a_1a_2.....a_n}

D

is na1+a2+....+an\frac{n}{a_1+a_2+....+a_n}

Answer

is a1+a2+....+ann\frac{a_1+a_2+....+a_n}{n}

Explanation

Solution

The correct option is(B): a1+a2+....+ann\frac{a_1+a_2+....+a_n}{n}