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k=lim(xtooo)[(sum(k=1)^(1000)(x+k)^(m))/...

`k=lim_(xtooo)[(sum_(k=1)^(1000)(x+k)^(m))/(x^(m)+10^(1000))]` (mgt101) is -

A

10

B

`10^(2)`

C

`10^(3)`

D

`10^(4)`

Text Solution

Verified by Experts

The correct Answer is:
C
`k=lim_( xtooo)[(x^(m)sum_(k=1)^(1000)(1+k/x)^(m))/(x^(m)(1+10^(1000)/(x^(m))))]`
`=(1+1+....+1)/(1)=1000`
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