Question

How do you use summation notation to expression the sum `7+14+28+...+896`?

Answer 1

`sum_(r=0)^(127) \ 7 + 7r \ \` or `\ \ sum_(r=1)^(128) 7r`

Explanation:

Let `S = 7+14+28+ ... + 896`

The first term is `7`, and we get subsequent terms by adding `7` each time, so the series is:

`S= 7 + (7+7) + (7+2(7)) + (7+3(7)) + ... 896`
`\ \ = 7 + (7+7) + (7+2(7)) + (7+3(7)) + ... (7+(127)7)`
`\ \ = sum_(r=0)^(127) \ 7 + 7r`

Alternatively if you prefer the sum to start from `r=1` we could write:

`S= (0+(1)7) + (0+(2)7) + (0+3(7)) + (0+(128)7)`
`\ \ = sum_(r=1)^(128) 7r`

(NB the sum evaluates to `S=57792`)