# What is a sample summation notation problem?

##### 1 Answer

Jan 13, 2017

You could be asked to find the sum of the first n Natural numbers.

These means the sum:

# S_n = 1 + 2 + 3 + 4 + ... #

We write this in shorthand summation notation as;

# sum_(r=1)^n r #

Where

# sum_(r=1)^n r =1/2n(n+1) #

So for example, If

# S_6 = sum_(r=1)^6 r = 1+2+3+4+5+6 #

We can determine by direct calculation that:

# S_6 = 21#

Or use the formula to get:

# S_6 = 1/2(6)(6+1) = (6xx7)/2 = 21#