Question

sum of the series 1 square - 2 X square + 3 square minus 4 square + 5 x square minus x square + up to 2n terms​

Answer 1

Answer:

The series is :-

1² - 2² + 3² - 4² +5² - 6² +7² - 8². . . .

Now,

We know that

A² - B² =(A+B) (A-B)

So,

1² - 2² =(1-2)(1+2) =3(-1) =(-3)

Now ,

In each such numbers - 1 will be constant as they are consecutive numbers.

Also,

If we consider 1² - 2² as 1st term of AP and 3² - 4² as second term and so on...

The AP will be as follows :-

(-3),(-7),(-11),(-15).....

Now ,

To understand this :-

(-3) has two numbers of the series...

Means if we have the AP (-3),(-7), (-11)... And we find the Sum of n terms of this AP we will get the sum of 2n terms of the series given above.

As each term of the AP has 2 terms of the series.

Now,

IN THE AP :-

A= (-3)

D = (-4)

Answer 2

Answer:

Step-by-step explanation: