Addition of squares and addition of Cubes

Addition of squares and addition of Cubes

The question may be running in your mind how to find the series addition of squares.

I think you have taken a small square number sequence.

Now let's take a square number sequence.

1² + 2² + 3² + 4² + 5²

Does this square number sequence end in 5?

This 5 is a number. The next number is 6 itself. It is another number. Add one to the double of 5. 5 × 2 + 1 = 11. This 11 is another no.

That is

End number of serial number (Not a squared number. A number to be squared)	5
Its next number is	6
Adding one to twice the final number is	5 × 2 + 1 = 11

Now multiply these three numbers and divide it by six.

Multiplying all three numbers gives 5 × 6 × 11 = 330

330 divided by six is ​​330 / 6 = 55

This 55 is the total.

Let's see if it is correct.

1² + 2² + 3² + 4² + 5² = 1 + 4 + 9 + 16 + 25 = 55

Isn't that right!

Now you can easily find the sum of squared numbers, can't you?

A formula for this will make the job easier. Suppose that the sequence of square numbers ends in n. So 1² + 2² + 3² + 4² + 5² + … + n²

Now the formula for that will be (n (n + 1) (2n + 1))/6

Remember only one thing here. n is not a square. Number to be squared. So n² is the square. n is the number to be squared.

Now we can write the formula like this?

1² + 2² + 3² + 4² + 5² + … + n² = (n (n + 1) (2n + 1))/6

Next I hear you asking how to find a way to find the addition of a cube number sequence. Let's see that today.

Let us take a numerical sequence of first 5 cube numbers.

1³ + 2³ + 3³ + 4³ + 5³

Let it be so. Now you know the addition of the normal number sequence from one to five.

That is

Addition of 1 + 2 + 3 + 4 + 5

As we have already seen.

Since it ends in five, multiply the five and the next number six and divide by two. The formula (n(n + 1))/2 gives (5 × 6)/2 = 15 doesn't it? Now find the square of 15. The answer is 225. This 225 is the addition of the sequence1³ + 2³ + 3³ + 4³ + 5³. What is surprising? So let's take a look.

1³ + 2³ + 3³ + 4³ + 5³ = 1 + 8 + 27 + 64 + 125 = 225 comes out right doesn't it?

So if you want to add a cube number sequence, just find the addition of its ordinary number sequence and square it. See how many surprises are packed into the Mathematics.

Now tell me the formula for this. Yes that's right.

1³ + 2³ + 3³ + 4³ + 5³ + … + n³ = (n(n + 1)/2)²

So we can go on and on about number sequences. Time goes enjoyably.

Addition of these series of numbers we add the numbers and form a formula with the relation between the numbers and the addition.

If you want to become a good math student, you need to learn some math techniques beyond this. That mathematical technique is algebra.

So you want to talk about that too? That's what we need to talk about.

Algebra can be intimidating for some people. You don't need such fear and hesitation. Because all the formulas you read and memorize for perimeter and area are algebraic formulas. So after looking at those formulas first, let's look at algebra.

Be ready for formulas for perimeter area tomorrow.

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