Sigma notation Problem set A

Evaluate each sum.

1. (a) \(\displaystyle\sum_{r=1}^{6}(4r - 1)\)
2. (b) \(\displaystyle\sum_{r=3}^{10}(2r + 7)\)
3. (c) \(\displaystyle\sum_{r=1}^{5} 2 \times 3^r\)
4. (d) \(\displaystyle\sum_{k=0}^{4} 5 \times 2^k\)

How many terms are there in \(\displaystyle\sum_{r=5}^{40} u_r\)?

Write each series in sigma notation.

1. (a) 6 + 11 + 16 + … + 101
2. (b) 3 + 6 + 12 + … + 768

Say whether \(\displaystyle\sum_{r=1}^{30}(100 - 3r)\) is arithmetic or geometric, and evaluate it.

Evaluate each sum.

1. (a) \(\displaystyle\sum_{r=1}^{20} 6\)
2. (b) \(\displaystyle\sum_{r=0}^{3} 5\times(-2)^r\)

Given that \(\displaystyle\sum_{r=1}^{n}(2r + 3) = 320\), find \(n\).

\(\text{Find the smallest } n \text{ for which }\displaystyle\sum_{r=1}^{n} 5\times 2^{r-1} > 3000\).