tmua.co.uk TMUA Mock Paper 1 · Question 5

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tmua.co.uk TMUA Mock Paper 1 · Q5

Paper 1Sequences & series

Consider the infinite series

S=\frac9{19}+\frac{99}{19^2}+\frac{999}{19^3}+\frac{9999}{19^4}+\cdots.

In each term, the numerator is formed by writing the digit 9 repeatedly, and the denominator is a higher power of 19. The series $S$ converges. What is the exact value of $S$ ?

\frac9{19}

1

\frac{20}{19}

\frac{19}{18}

\frac{10}{9}

\frac{19}{9}

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