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DPiD Maths Mock Set 1 Paper 1 · Q10

Paper 1Number & counting

Let an=n⋅2n+1(n+1)(n+2)\displaystyle a_n=\frac{n\cdot2^{n+1}}{(n+1)(n+2)}, where nn is a positive integer. Find a1+a2+a3+⋯+a254a_1+a_2+a_3+\cdots+a_{254}.

A2256256\frac{2^{256}}{256}
B2256256−2\frac{2^{256}}{256}-2
C−2-2
D2256256+2\frac{2^{256}}{256}+2
E22
F2255255−2\frac{2^{255}}{255}-2
G2256255−2\frac{2^{256}}{255}-2
H2254256−2\frac{2^{254}}{256}-2

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