Review question

# Can we sum from $1000$ to $2000$ excluding multiples of 5? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R7424

## Question

1. Prove that the sum of all the integers between $m$ and $n$ inclusive ($m, n \in \mathbb{Z}_+$, $n > m$) is $\tfrac{1}{2}(m+n)(n-m+1)$. Find the sum of all the integers between $1000$ and $2000$ which are not divisible by $5$.

2. A geometric series has first term $2$ and common ratio $0.95$. The sum of the first $n$ terms of the series is denoted by $S_n$ and the sum to infinity is denoted by $S$. Calculate the least value of $n$ for which $S - S_n < 1$.