Question

What is the sum of Even Numbers 38 to 88?​

Answer 1

Answer:

38 Into 2 =76 is the answer

Answer 2

Step-by-step explanation:

: I am considering 2 and 42 are included.

Let’s take a small example in a way shown below to achieve a generalized formula:

2 + 4 + 6 + … + 2n = s

Where n is the nth even number, for example, second even number (n = 2) is 4, so 2n gives the even number. And s is the sum.

Now we will add to this equation a copy of the same equation with all terms in reverse, such as:

2 + 4 + 6 + … + 2n = s

2n + (2n - 2) + (2n - 4) + … + 2 = s

We will adding both the equations, meaning we will be adding the first term of the first equation with the first term of the second equation, such as 2 + 2n, and so on. And also remember to add the s in the RHS of both equations. So it will give:

(2 + 2n) + (2 + 2n) + … + (2 + 2n) = 2s

We now understand “(2 + 2n)” is repeated n times. So we can simplify it further like this:

(2 + 2n) × n = 2s

We can take “2” common from (2 + 2n) like:

2n(n + 1) = 2s

Now it’s possible to divide both the LHS and RHS of the equation with 2, so it gives:

n(n + 1) = s, where s is the final sum of the even numbers from 2 to 2n.

In your case, 2n is 42, so n would be 42/2, which is 21.

Result: 21 × (21 + 1) is your answer!

Which is 21 × 22, equaling to 462.