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BINOMIAL THEOREM | BINOMIAL INSIDE BINOMIAL, SUM OF THE SERIES WHEN I AND J ARE INDEPENDENT | Find the `sum_(r=0)^n (n+r)C_r`, Sum of the series when i and j are independent, Find the sum (i)`sum_(0lei < jlen)sum . ^ nC_i .^ nC_j` (ii)`sum_(0lei le jlen)sum . ^ nC_i .^ nC_j`(iii)`sum_(i!=j).^ nC_i .^ nC_j`, Find the value of `sum_(0leiltjlen) (C_i+C_j)`, Find the sum: `sum_(0leiltjlen) j. ^nC_i`

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