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tmua.me Medium Set C Paper 1 · Q12

Paper 1Sequences & series

A sequence is defined by

u1=3,un+1=un(un+1)(n≥1).u_1=3,\qquad u_{n+1}=u_n(u_n+1)\quad(n\geq1).

Let M=u10M=u_{10}. Which of the following is equal to

1u1+1+1u2+1+⋯+1u9+1 ?\frac1{u_1+1}+\frac1{u_2+1}+\cdots+\frac1{u_9+1}\,?
A1M\dfrac1M
B13−1M+1\dfrac13-\dfrac1{M+1}
C1−3M1-\dfrac3M
D13−1M\dfrac13-\dfrac1M
E13−1M(M+1)\dfrac13-\dfrac1{M(M+1)}
F13\dfrac13

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