Sum of k

How to solve the given summation by using the sum of k formula: formula, 1 example, and its solution.

Formula

Formula

The sum of k, as k goes from 1 to n, is
n(n + 1)/2.

This means
1 + 2 + 3 + ... + n = n(n + 1)/2.

You can prove this formula
by using mathematical induction.

Example

Example

Solution

The coefficient 4 gets out from the sigma.
k is in the sigma.

-3 is a constant.
So write -3n.

Summation: How to Solve

Write the coefficient 4.

The sum of k is
n(n + 1)/2.

And write -3n.

So 4⋅n(n + 1)/2 - 3n.

Cancel the denominator 2
and reduce the numerator 4 to, 4/2, 2.

2⋅n(n + 1) = 2n2 + 2n

+2n - 3n = -n

So 2n2 - n is the answer.