Review question

When does the sum of this series first exceed $2999/4000$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7487

Suggestion

Find the sum of $n$ terms of the geometric progression $\frac{1}{2}+\frac{1}{6}+\frac{1}{18}+\dotsb.$

What is the common ratio of this geometric series?

What is the $n$th term of this geometric series?

Let $S_n$ denote the sum of the first $n$ terms. Could we write the expansion of $\frac{1}{3}S_n$ underneath the expression for $S_n$?

What do we notice? What happens if we take the two expressions away from each other?

Deduce the sum to infinity of this series.

When $n\to \infty$, what does $S_n$ tend towards?

Find the least number of terms of the series which must be taken for their sum to exceed $\dfrac{2999}{4000}$.

Could we try to find an $n$ such that $S_n = \dfrac{2999}{4000}$?

Could we write down the first few powers of $3$?