Find the sum 1 xx 2 xx .^(n)C(1) + 2 xx ...

Find the sum `1 xx 2 xx .^(n)C_(1) + 2 xx 3 xx .^(n)C_(2) + "….." + n xx (n+1) xx .^(n)C_(n)`.

`(3^(n)+(-1)^(n))/(2)`

`(3^(n)-(-1)^(n))/(2)`

`(3^(n) + 1)/(2)`

`(3^(n) - 1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:

`(1+2)^(n) - (1-2)^(n) = 2[.^(n)C_(1)xx2+.^(n)C_(3)xx2^(3)+.^(n)C_(5)xx2^(5)+"….."]`
`:. .^(n)C_(1)xx2+.^(n)C_(3)xx2^(3)+.^(n)C_(5)xx2^(5)+"…."= (3^(n)-(-1)^(n))/(2)`

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