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Official Specimen Paper 2 · Q16

Paper 2Sequences & series

The sequence ana_n is given by the rule:

a1=2a_1=2
an+1=an+(−1)nfor n≥1.a_{n+1}=a_n+(-1)^n\quad\text{for }n\ge1.

What is

∑n=1100an?\sum_{n=1}^{100}a_n?
A150150
B250250
C−4750-4750
D51505150
E4(1−(12)100)4\left(1-\left(\frac12\right)^{100}\right)
F4((32)100−1)4\left(\left(\frac32\right)^{100}-1\right)

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