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Find the sum Sigma(j=1)^(n) Sigma(i=1)^...

Find the sum `Sigma_(j=1)^(n) Sigma_(i=1)^(n) I xx 3^j`

Text Solution

Verified by Experts

The correct Answer is:
`(3n(3^n-1)(n+1))/(4)`
`sum_(j=1)^(n)sum_(i=1)^(n)ixx3^(j)=(sum_(j=1)^(n)3^(j))(sum_(i=1)^(n)i)`
`=(3+3^(2)+3^(3)+….+3^(n))xx(1+2+3+..+n)`
`(3(3^(n)-1))/(3-1)xx(n(n+1))/2`
`=(3n(3^(n)-1)(n+1))/4`
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