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If 1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-...

If `1/(sqrt(4x+1)){((1+sqrt(4x+1))/2)^n-((1-sqrt(4x+1))/2)^n}=a_0+a_1x` then find the possible value of `ndot`

Text Solution

Verified by Experts

The correct Answer is:
`n=11` or `12`
We have, `(1)/(sqrt(4x+1)) ={((1+sqrt(4x+1))/(2))^(n)-((1-sqrt(4x-1))/(2))^(n)}`
`= (1)/(2^(n)sqrt(4x+1)){2[.^(n)C_(1)sqrt(4x+1)+.^(n)C_(3)(sqrt(4x+1))^(3)+"....."]}`
`= (1)/(2^(n-1))[.^(n)C_(1)+.^(n)C_(3)(sqrt(4x+1))^(2)+.^(n)C_(5)(sqrt(4x+1))^(4)+"....."]`
Since R.H.S. of the given expression contains `x^(5)`. so this expression should go up to `(sqrt(4x+1))^(10)` and hence `n = 11` or `12`.
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