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Value of sum(k=1)^oosum(r=0)^k1/(3^k)(^k...

Value of `sum_(k=1)^oosum_(r=0)^k1/(3^k)(^k C_r)` is `2/3` b. `4/3` c. `2` d. `1`

A

`2/3`

B

`4/3`

C

`2`

D

1

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(k=1)overset(oo)sumunderset(r=0)overset(k)sum(1)/(3^(4))(.^(k)C_(r))=underset(k=1)overset(oo)sum(1/(3^(k))(underset(k=0)overset(k)sum.^(k)C_(r)))`
`= underset(k=1)overset(oo)sum((2^(k))/(3^(k)))`
`= 2/3+(2/3)^(2)+"....."oo`
`= (2//3)/(1-2/3) = 2`
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