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Official 2017 Paper 1 · Q17

Paper 1CalculusSequences & seriesNumber & counting

The two functions F(n)F(n) and G(n)G(n) are defined as follows for positive integers nn:

F(n)=1n∫0n(n−x) dxF(n)=\frac1n\int_0^n(n-x)\,\dd x
G(n)=∑r=1nF(r)G(n)=\sum_{r=1}^nF(r)

What is the smallest positive integer nn such that G(n)>150G(n)>150?

A2222
B2323
C2424
D2525
E2626

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