Cr+1m+∑k=mnCrk=
Cr+1n
Cr+1n+1
Crn
None of these
Explanation for the correct option:
Finding the value of Cr+1m+∑k=mnCrk :
Formula to be used : According to the binomial theorem, mCr+mCr+1=m+1Cr+1.
Then,
mCr+1+∑k=mnCrk=mCr+1+mCr+m+1Cr+m+2Cr+...+nCr+1
=mCr+1+mCr+m+1Cr+m+2Cr+...+nCr[∵nCr+nCr-1=n+1Cr]=m+1Cr+1+m+1Cr+m+2Cr+...+nCr=m+1Cr+1+m+1Cr+m+2Cr+...+nCr=m+2Cr+1+m+2Cr+...+nCr⋮=nCr+1+nCr=n+1Cr+1
Hence, option (B) is the correct answer.