For every integer \(n\) from \(1\) to \(200,\) inclusive, the \(nth\) term of a certain sequence is given by

For every integer \(n\) from \(1\) to \(200,\) inclusive, the \(nth\) term of a certain sequence is given by \((-1)^n\cdot 2^{-n}.\) If \(N\) is the sum of the first \(200\) terms in the sequence, then \(N\) is

(A) less than \(-1\)

(B) between \(-1\) and \(-\dfrac12\)

(C) between \(-\dfrac12\) and \(0\)

(D) between \(0\) and \(\dfrac12\)

(E) greater than \(\dfrac12\)

Answer: C

Source: Veritas Prep