he sum of the series 105 ²  − 103 ²  + 104 ²  − 102 ²  + 103 ²  − 101 ²  + 102 ²  − 100 ²  + … up to 40 terms is

	A :		5 520
	B :		5 560
	C :		7 500
	D :		7 560

 

plz explain this sum

We appreciate your bringing the error to our notice. We shall most definitely try and ensure that such errors do not occur in the future.

The correct solution of the question is as follows:

The given series is,

105² – 103² + 104² – 102² + 103² – 101² + 102² – 100² + ... (up to 40 terms)

The given series can be written as,

(105 – 103) (105 + 103) + (104 – 102) (104 + 102) + (103 – 101) (103 + 101) + ... (up to 20 terms) = S₂₀ (say)

∴ S₂₀ = (105 + 103)2 + (104 + 102)2 + (103 + 101)2 + (102 + 100)2 + ... (up to 20 terms)

= 2 [105 + 104 + 103 + 102 + ... (up to 20 terms)] + 2 [103 + 102 + 101 + 100 + ... (up to 20 terms)]

Thus, the sum of the given series is 7560.