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The value of sum(r=0)^(n) sum(p=0)^(...

The value of `sum_(r=0)^(n) sum_(p=0)^(r) ""^(n)C_(r) . ""^(r)C_(p)` is equal to

A

`3^(n) - 2^(n)`

B

`3^(n) - 2^(n) - 2`

C

`3^(n) - 2^(n) + 2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
d
We have ,
`sum_(r=0)^(n) sum_(r=0)^(n) ""^(n)C_(r) . ""^(r)C_(p)`
`sum_(r=0)^(n) ""^(r)C_(p) (sum_(r=0)^(n) ""^(n)C_(p)) = sum_(r=0)^(n) . ""^(n)C_(r) 2^(r) = (1 +2)^(n) = 3^(n)` .
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OBJECTIVE RD SHARMA ENGLISH-BINOMIAL THEOREM AND ITS APPLCIATIONS -Section I - Solved Mcqs
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