1.

Find the sum of C_1 + 2C_2 + 3C_3 + .... + nC_n

Answer»

SOLUTION :`C_1 + 2C_2 + 3C_3 + .... + nC_n`
= `sum_(k=1)^N kC_k` = `sum_(k=1)^n k.^nC_k` = `sum_(k=1)^n n("^(n-1)C_(k-1))`
`nsum_(k=1)^n "^(n-1)C_(k-1)
= `n("^(n-1)C_0 + ^(n-1)C_1 + .... + ^(n-1)C_(n-1))`
`n.2^(n-1)`


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