TMUA 2017 Paper 2 Q6 — Worked Solution

P2·Integration, Sequences & Series·5.5Official · 2017 · Q6

recursive-integralgeometric-sequenceconstant-multiplier

A sequence

u_{0}, u_{1}, u_{2}, \dots

is defined as follows:

u_{0} = 1, u_{n} = \int_{0}^{1} 4 x u_{n - 1} d x for n \geq 1.

What is the value of

u_{1000}

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