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