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Algebra Level 3

What is the sum of the first $2016$ even numbers .

Important: The first even number will be $2$ .

This problem is inspired with the "odd version of this", which is probably not original.

3 solutions

A Former Brilliant Member
Jan 15, 2016

$\rightarrow$ $\text{Sum of first n even numbers}=$ $n(n+1)$
$\Rightarrow 2016×2017=\boxed{4066272}$

Sum of first n even numbers only n(n+1).You hasn't mentioned it.Please mention it

Vishal S - 5 years, 5 months ago

Mentioned now!

A Former Brilliant Member - 5 years, 5 months ago

Ayushman Chahar
Jan 16, 2016

This can be done by using Arithmatic Progression

Milan Milanic
Jan 15, 2016

Solution:

Mathematical induction:

$S(1) = 2;$

$S(2) = 2 + 4 = 6;$

$S(3) = 2 + 4 + 6 = 12;$

$...$

It seems that $S(n) = n(n + 1)$ . If so, then: $S(n + 1) = 2 + 4 + ... + 2n + 2n + 2 = n(n + 1) + 2(n + 1) =$ $= (n + 2)(n + 1)$ .

Therefore, the solution is $2016 \times 2017 = \boxed{4066272}$ .