Problema Solution

Conjecture for the Sum of the first 100 positive even numbers

Answer provided by our tutors

First, let us consider the sum of the first 100 numbers (even and odd). You could arrange them into 50 groups of two adding up to 101 (ex. 1+100=101, 2+99=100, etc). Therefore the sum would be:

50(101)=5050


Now, let us consider the sum of the first 100 even numbers (2, 4, 6, ......... 200). This will be double the sum of the first 100 numbers. Therefore the sum would be:

2(5050)=10100


Alternately, we could have followed our first line of reasoning and arrange the even numbers into 50 groups of two adding up to 202. Then we would write the sum as:

50(202)=10100