# Find an easy way to evaluate the following series: #3+5+7+cdots+ 17+19+21#?

##### 1 Answer

Apr 17, 2016

#### Explanation:

Note that as you work inwards, groups of

Add the first and last numbers,

Since the next two numbers inwards are just

#5+19=(3+2)+(21-2)=(3+21)+(2-2)=24#

The pattern continues:

#{(3+21=24),(5+19=24),(7+17=24),(9+15=24),(11+13=24):}#

Thus, the sum is