TMUA 2016 Paper 2 Q6 — Worked Solution

P2·Sequences & Series, Differentiation·6.5Official · 2016 · Q6

recursive-functionsgeometric-seriespattern

The sequence of functions

f_{1} (x), f_{2} (x), f_{3} (x), \dots

is defined as follows:

f_{1} (x) = x^{10}

and

f_{n + 1} (x) = x f_{n}^{'} (x)

for

n \geq 1

, where

f_{n}^{'} (x) = \frac{d f _{n} ( x )}{d x}

. Find the value of

n = 1 \sum 20 f_{n} (x)

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