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Euclid Sample Paper 1 · Q15

Paper 1Sequences & seriesNumber & counting

For each integer kk satisfying

−4≤k≤4,-4\leq k\leq4,

consider the two curves

y=2xandy=(−1)kx+k.y=2^x\qquad\text{and}\qquad y=(-1)^kx+k.

Let NkN_k be the number of points of intersection of these two curves. Find

∑k=−44Nk.\sum_{k=-4}^{4}N_k.
A44
B55
C66
D77
E88
F99
G1010
H1212

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