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If sn= sum(r=0)^n 1/(^"nCr) and tn=sum(r...

If `s_n= sum_(r=0)^n 1/(^"nC_r)` and `t_n=sum_(r=0)^n r/("^nC_r)` then `t_n/s_n` is equal to

A

a. `n = 1`

B

b. `n = 2`

C

c. `n = 3`

D

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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