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If sum(r=0)^nr/(^n Cr)=sum(r=0)^n(n^2-3n...

If `sum_(r=0)^nr/(^n C_r)=sum_(r=0)^n(n^2-3n+3)/(2.^n C_r)` , then a.`n=1` b. `n=2` c. `n=3` d. none of these

A

`n = 1`

B

`n = 2`

C

`n = 3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, C
`underset(r=0)overset(n)sum(r)/(.^(n)C_(r)) = underset(r=0)overset(n)sum(n-r)/(.^(n)C_(n-r))= n/2underset(r=0)overset(n)sum(1)/(.^(n)C_(r))`
`:. n/2 = (n^(2)-3n+3)/(2)`
or `n = 1,3`
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