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Show that x^(n) =1 + n(1 -1/x) + (n(n+1)...

Show that `x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...`

A

`x^(n)`

B

`x^(-n)`

C

`(1-1/x)^(n)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`1+n(1-1/x) + (n(n+1))/(2!) (1-1/x)^(2)+"…."oo`
`= 1-n[-(1-1/x)]+(-n(-n-1))/(2!)[-(1-(1)/(x))]^(2)+"....."oo`
`= [1-(1-(1)/(x))]^(-n)`
`= x^(n)`
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  6. If a(n) = sum(r=0)^(n) (1)/(""^(n)C(r)), then the value of (sumsum)(0l...

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  7. In the expansion of [(1+x)//(1-x)]^2, the coefficient of x^n will be 4...

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  8. Show that x^(n) =1 + n(1 -1/x) + (n(n+1))/1.2 (1 -1/x)^(2) + ...

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  15. If |x|<1, then find the coefficient of x^n in the expansion of (1+x+x^...

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  16. If x is positive, the first negative term in the expansion of (1 + x)^...

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  17. If x is so small that x^(3) and higher power of x may neglected, then ...

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  18. If the expansion in power of x of the function (1)/(( 1 - ax)(1 - b...

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