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find the sum of series nC1+(n+1)C2+(n+2)C3+.........+(n+r-1)Cr please could u help me how to proceed in these type of problems
Arun KumarIIT DelhiAskiitians Faculty
Little mistake in above answer
N(C1+C2+......Cr)+( (2-1)C2+(3-1)C3......) SUMMATION Cr + SUMMATION rCrSUMMATION Cr is 2^nAnd to solve rCr write expansion of (1+x)^n and differentiate and then put x=1
Dear student,Please find the solution to your problem. nC1 + n+1C2 + n+2C3 + .........+ n+r–1Cr= nC0 + nC1 + n+1C2 + n+2C3 + .........+ n+r-1Cr – nC0 {adding and subtracting nC0}= n+1C1 + n+1C2 + n+2C3 + .........+ n+r-1Cr – 1{Since we know, nCr + nCr+1 = n+1Cr+1}= n+2C2 + n+2C3 + .........+ n+r-1Cr – 1With each term we can apply the same formulaHence, the condensed result will be= n+rCr – 1 = n+rCn – 1 Thanks and regards,Kushagra
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