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 – 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
