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StepMaths Mock Paper 2 · Q6

Paper 2CalculusSequences & series

Two sequences are related by the following relationships:

un+1=xun,u1=1qn=d(un)dxu_{n+1}=xu_n,\quad u_1=1\qquad q_n=\frac{\mathrm{d}(u_n)}{\mathrm{d}x}

Find the value of

∫0x∑n=1∞qndx\int_0^x\sum_{n=1}^{\infty}q_n\dd x

if ∣x∣<1|x|<1.

Axx
Bx1−x\dfrac{x}{1-x}
C11−x\dfrac1{1-x}
DThe integral is not defined
EWe cannot tell if the integral is defined

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