To obtain the alternating sum directly from the expansion of

MATHEMATICS · Single correct · A Level · Mathematics · Sequences and series · Sequences and series

Problem

To obtain the alternating sum

\displaystyle \sum_{k=0}^{n} (-1)^k {n\choose k}

directly from the expansion of

(a+b)^n

, which choice of

(a,\,b)

is appropriate? (a)

a=1,\;b=1

(b)

a=-1,\;b=1

(c)

a=1,\;b=-1

(d)

a=0,\;b=1