The sum of the first $n$ terms of a sequence is given by $S_n = 4 - \frac{(-1)^n}{4^{n-1}}$. Fin

Question

The sum of the first $n$ terms of a sequence is given by $S_n = 4 - \frac{(-1)^n}{4^{n-1}}$. Find an expression for the $n$ th term of the sequence and show that the sequence is a geometric progression. Find the sum to infinity, $S$, of the progression and the least value of $n$ for which the magnitude of the difference between $S_n$ and $S$ is less than $0.001$.

Accepted Answer

(i) $u_n=-20\left(-\dfrac14\right)^n$, with common ratio $-\dfrac14$ (ii) $S=4$, least $n=6$

2007 NJC Promo Q7

2007 NJC Promo Q7

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