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DPiD Maths Mock Set 1 Paper 2 · Q19

Paper 2Sequences & seriesNumber & counting

Find

∑k=0∞⌊1+8 000 0004k2⌋,\sum_{k=0}^{\infty}\left\lfloor\frac{1+\sqrt{\dfrac{8\,000\,000}{4^k}}}{2}\right\rfloor,

where ⌊x⌋\lfloor x\rfloor denotes the largest integer less than or equal to xx.

A28262826
B28282828
C28302830
D14141414
E28322832
F200022000\sqrt2
G28242824
H28362836

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