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Question

Question: The coefficient of x<sup>m</sup> in (1 + x)<sup>m</sup> + (1 + x)<sup>m +1</sup> + ...... + (1 + x)...

The coefficient of

xm in (1 + x)m + (1 + x)m +1 + ...... + (1 + x)n, m £ n is :

A

n+1Cm+1

B

n –1Cm–1

C

nCm

D

nCm+1

Answer

n+1Cm+1

Explanation

Solution

mCm + m+1Cm + ......... + nCm

= m+1Cm+1 + m+1Cm+.........+ nCm

= m+2Cm+1 + m+2Cm + ...... + nCm

= ........................................

nCm+1 + nCm = n+1Cm+1