3A. Compute the simplified numerical value of the expression: (4042 + 4040 + 4038 + … + 6 + 4 + 2) −(4041 + 4039 + 4037 + … + 5 + 3 + 1).

The simplified numerical value of the expression: (4042 + 4040 + 4038 + … + 6 + 4 + 2) −(4041 + 4039 + 4037 + … + 5 + 3 + 1) is 2021 and this can be determined by using the properties of arithmetic progression.

Given :

Expression --  (4042 + 4040 + 4038 + … + 6 + 4 + 2) −(4041 + 4039 + 4037 + … + 5 + 3 + 1)

Let the given expression be written in the form of two arithmetic progressions. That is:

where is (4042 + 4040 + 4038 + … + 6 + 4 + 2) and is (4041 + 4039 + 4037 + … + 5 + 3 + 1).

First, determine the number of terms in progression and .

For progression :

-4040 = -2(n - 1)

2020 = n - 1

2021 = n

For progression :

-4040 = -2(n - 1)

2020 = n - 1

n = 2021

Sum of n terms for progression .

Sum of n terms for progression .

Now, the value of the expression is:

= 4086462 - 4084441

= 2021

So, the simplified numerical value of the expression: (4042 + 4040 + 4038 + … + 6 + 4 + 2) −(4041 + 4039 + 4037 + … + 5 + 3 + 1) is 2021.

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The value of the expression is 2021

Step-by-step explanation:

Compute the numerical value of the expression

(4042 + 4040 + 4038 + … + 6 + 4 + 2) - (4041 + 4039 + 4037 + … + 5 + 3 + 1).

Rearranging the positive and negative terms:

(4042-4041)+(4040-4039)+(4038-4037)+...(2-1)

All the partial subtractions are 1:

1 + 1 + 1 + + 1

This sequence is repeated 4042/2=2021 times, thus the value of the expression is 2021

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