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Grade:

                        

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

6 years ago

Answers : (4)

Arun Kumar
IIT Delhi
askIITians Faculty
256 Points
							

Arun Kumar
IIT Delhi
Askiitians Faculty
6 years ago
Arun Kumar
IIT Delhi
askIITians Faculty
256 Points
							Little mistake in above answer

6 years ago
Saumya
13 Points
							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
						
2 years ago
Kushagra Madhukar
askIITians Faculty
605 Points
							
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 – nC      {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 – 1
With each term we can apply the same formula
Hence, the condensed result will be
= n+rCr – 1 = n+rCn – 1
 
Thanks and regards,
Kushagra
4 months ago
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