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

Oct 14, 2017

$5 {\sum}_{r = 1}^{n} \left(\frac{1}{1 + r}\right)$

#### Explanation:

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

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

$\frac{5}{1 + r} + \frac{5}{1 + r} = \frac{5}{1 + \left(r = 1\right)} + \frac{5}{1 + \left(r = 2\right)} = \frac{5}{1 + 1} + \frac{5}{1 + 2} + \ldots + \frac{5}{1 + n}$

${\sum}_{r = 1}^{n} \left(\frac{5}{1 + r}\right) = {\sum}_{r = 1}^{n} 5 \left(\frac{1}{1 + r}\right)$

We can factor out the 5:

$5 {\sum}_{r = 1}^{n} \left(\frac{1}{1 + r}\right)$