Question

How do you use sigma notation to write the sum for `5/(1+1)+5/(1+2)+5/(1+3)+...+5/(1+15)`?

Answer 1

`5sum_(r=1)^(n)(1/(1+r))`

Explanation:

We only need to represent the changing quantity, so let r represent this:

if `r =1, r=2 , r=3` etc:

`5/(1+r) + 5/(1+r)= 5/(1+(r=1)) + 5/(1+(r=2))= 5/(1+1)+5/(1+2)+...+5/(1+n)`

`sum_(r=1)^(n)(5/(1+r))=sum_(r=1)^(n)5(1/(1+r))`

We can factor out the 5:

`5sum_(r=1)^(n)(1/(1+r))`