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Euclid Sample Paper 1 · Q4

Paper 1Logic & proofNumber & counting

For each positive integer nn, define

an=n(n+1−n).a_n=\sqrt n\left(\sqrt{n+1}-\sqrt n\right).

Which of the following is true for every positive integer nn?

A0<an≤250<a_n\leq\frac25
B25<an<12\frac25<a_n<\frac12
C12<an<35\frac12<a_n<\frac35
D35<an<1\frac35<a_n<1
Ean>1a_n>1

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