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Official 2017 Paper 2 · Q6

Paper 2CalculusSequences & series

A sequence u0u_0, u1u_1, u2u_2, …\ldots is defined as follows:

u0=1u_0=1
un=∫014xun−1 dxfor n≥1u_n=\int_0^1 4xu_{n-1}\,\dd x\quad\text{for }n\geq1

What is the value of u1000u_{1000}?

A210002^{1000}
B410004^{1000}
C41000!\frac4{1000!}
D41001!\frac4{1001!}
E210001000!\frac{2^{1000}}{1000!}
F410001000!\frac{4^{1000}}{1000!}
G210001001!\frac{2^{1000}}{1001!}
H410001001!\frac{4^{1000}}{1001!}

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