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Official 2021 Paper 2 · Q20

Paper 2CalculusSequences & series

A sequence of functions f1,f2,f3,…f_1,f_2,f_3,\ldots is defined by

f1(x)=∣x∣f_1(x)=|x|
fn+1(x)=∣fn(x)+x∣for n≥1.f_{n+1}(x)=|f_n(x)+x|\qquad\text{for }n\ge1.

Find the value of

∫−11f99(x)dx.\int_{-1}^1f_{99}(x)\dd x.
A00
B0.50.5
C11
D49.549.5
E5050
F9999
G99.599.5
H100100

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