examday

tmua.me papers

tmua.me Medium Set A Paper 1 · Q19

Paper 1Sequences & seriesNumber & counting

A sequence of positive numbers is defined by

u1=12,uk+1=uk1+uk(k≥1).u_1=\frac12,\qquad u_{k+1}=\frac{u_k}{1+u_k}\quad(k\geq1).

For a positive integer nn,

unun+1=1156.u_nu_{n+1}=\frac1{156}.

What is the value of

1u1+1u2+⋯+1un ?\frac1{u_1}+\frac1{u_2}+\cdots+\frac1{u_n}\,?
A6666
B7676
C7777
D7878
E9090
F156156

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →