Sum of Squares and Square of Sum Between Two Numbers Calculator

Welcome to the sum of squares and square of the sum between two numbers calculator. This calculation solves two problems: one is the sum of squares of the integers in the interval, and the other is the square of the sum of the integers in the interval.

Sum of Squares and Square of Sum Between Two Numbers Calculator

The sum of squares between and the square of the sum between a and b.

Eg, The sum of squares between and the square of the sum between 10 and 20? Enter 10 in the first input box and enter 20 in the second input box, then click Calculate button.

Calculate Reset

What is the sum of squares of the integers in the interval?

The interval sum of squares is the sum of squares of all integers in the interval.

The expression for the interval sum of squares is

n₁² + n₂² + n₃² + n₄²……

For example, the sum of squares between 10 and 20.

The numbers between 10 and 20 are 11, 12, 13, 14, 15, 16, 17, 18 and 19. The sum of squares of them is

11² + 12² + 13² + 14² + 15² + 16² + 17² + 18² + 19² = 121 + 144 + 169 + 196 + 225 + 256 + 289 + 324 + 361 = 2085

What is the square of the sum of the integers in the interval?

The square of the interval sum is the square of the sum of all integers in the interval. The expression for the square of the interval sum is

(n₁ + n₂ + n₃ + n₄……)²

For Example, the square of the sum between 10 and 20.

The sum of them is

11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 = 135

The square of the sum is

135² = 18225

So, the square of the sum between 10 and 20 is 18225. It is not the same as the interval sum of squares.

How to use the calculator to calculate the sum of squares and the square of the sum in the interval

Using the calculator is simple, follow these 3 steps:

1Enter the starting number in the first input box.
2Enter the ending number in the second input box.
3Click Calculate button to get the answer, or click Reset button to start a new calculation.

Note that it is between two numbers, so the starting and ending numbers are not included.

Next, let’s look at some examples.

Solved examples using the sum of squares and square of sum between two numbers calculator

Example 1: What are the sum of squares and the square of the sum between 1 and 100?

Enter 1 in the first input box.

Enter 100 in the second input box.

Then click Calculate button, as shown in the figure, the sum of squares of them is 328349, and the square of the sum of them is 24492601.

What are the sum of squares and the square of the sum between 1 and 100?

Example 2: What are the sum of squares and the square of the sum between 20 and 30?

Enter 20 in the first input box.

Enter 30 in the second input box.

Then click Calculate button, as shown in the figure, the sum of squares of them is 5685, and the square of the sum of them is 50625.

What are the sum of squares and the square of the sum between 20 and 30?

Sum of Squares and Square of Sum Between Two Numbers Calculator