Question

(30^2-29^2)+(28^2-27^2)+........(2^2-1^2)=?

Answer 1

Answer:

After solving it using the identity a²-b²= (a+b)(a-b) we will get the equation as

59+55+........+3

Here a = 55, d = -4, an = 3

an = a+(n-1)d

3 = 55+(n-1)(-4)

3 = 55-4n+4

4n = 56

n = 19

Now sum of all these terms = n/2(a+l)

= 19/2(55+3)

= 19/2× 58

= 19×29

= 551

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