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OxbridgeMind TMUA Paper 1 · Q8

Paper 1Sequences & series

Let Fk=Fk−1+Fk−2F_k=F_{k-1}+F_{k-2} where F0=0F_0=0, F1=1F_1=1. Define the series s(x)=∑k=1∞Fkxks(x)=\displaystyle\sum_{k=1}^{\infty}\dfrac{F_k}{x^k} for x>2x>2. What is the value of s(x)s(x)?

Ax2x2−x−1\dfrac{x^2}{x^2-x-1}
Bxx2−x−1\dfrac{x}{x^2-x-1}
C1x2−x−1\dfrac1{x^2-x-1}
Dx−1x-1
Ex2−1x\dfrac{x^2-1}{x}

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