Question 103322
Before we start, let's be clear. 
Positive integers are 1,2,3,4,5,.... and do not include zero. Consecutive means one right after the other (3 and 4 are consecutive integers). 
What is the smallest sum from one positive integer? 
1
What is the smallest sum from two consecutive positive integers?
1+2=3 Sum from 1 to 2. 
What is the smallest sum from three consecutive positive integers?
1+2+3=6 Sum from 1 to 3.
There's a pattern here.  
...
What is the smallest sum from ten consecutive positive integers?
The sum from 1 to 10.
1+2+3+4+5+6+7+8+9+10=55
What is the smallest sum from eleven consecutive positive integers?
The sum from 1 to 11.
Or the sum from 1 to 10 plus 11. 
1+2+3+4+5+6+7+8+9+10+11=55+11=66
What is the smallest sum from twelve consecutive integers?
The sum from 1 to 12.
Or the sum from 1 to 11 plus 12. 
1+2+3+4+5+6+7+8+9+10+11+12=66+12=78