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lim(xrarroo) (sum(r=1)^(10)(x+r)^(2010))...

`lim_(xrarroo) (sum_(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))=`

A

5

B

2010

C

`(502)/(1005)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
`underset(xrarroo)(lim)(sum_(r=1)^(10)(x+r)^(2010))/((x^(1006)+1)(2x^(1004)+1))`
`" =underset(xrarroo)(lim)((x+1)^(2010)+(x+2)^(2010)+...+(x+10)^(2010))/((x^(1006)+1)(2x^(1004)+1))`
`" "=underset(xrarroo)(lim)((1+(1)/(x))^(2010)+(1+(2)/(x))^(2010)+....+(1+(10)/(x))^(2010))/((1+(1)/(x^(1006)))(2+(1)/(x^(1004))))`
`=(10)/(2)=5`
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