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tmua.co.uk TMUA Mock Paper 1 · Q11

Paper 1Sequences & seriesPowers & logarithmsNumber & counting

The sum SnS_n is defined by

Sn=∑r=1nlog⁡2(1+2r+3r(r+2)).S_n=\sum_{r=1}^n\log_2\left(1+\frac{2r+3}{r(r+2)}\right).

Find the smallest integer nn such that Sn≥4+log⁡25S_n\ge4+\log_2 5.

A77
B88
C1212
D1313
E1414
F1515
G1919

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