Question

How do you use summation notation to expression the sum `5+15+45+...+3645`?

Answer 1

`5+15+45+...+3645 = sum_(r=0)^6 \ 3^r*5= 5 \ sum_(r=0)^6 \ 3^r`

Explanation:

Let the given summation be denoted by `S`

Then:

`S = 5+15+45+...+3645`
`\ \ \= 5+3*5+9*5+...+729*5`
`\ \ \= 3^0*5+3^1*5+3^2*5+...+3^6*5`
`\ \ \= sum_(r=0)^6 \ 3^r*5`
`\ \ \= 5 \ sum_(r=0)^6 \ 3^r`