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(vi) (x - y)?, (x² + y²), (x + y)2 ..., to n terms |
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Answer» -STEP explanation:We have to find the sum of (x−y) 2 ,(x 2 +y 2 ),(x+y) 2 ,... to N termsFrom the progression we know that first term is a=(x−y) 2 Now, let's CALCULATE the common difference dd=a 2 −a 1 =(x 2 +y 2 )−(x−y) 2 =(x 2 +y 2 )−(x 2 +y 2 −2xy) =x 2 +y 2 −x 2 −y 2 +2xy=2xyWe know that the sum of an A.P is given by S n = 2n ×{2a+(n−1)d}So,S n = 2n ×{2(x−y) 2 +(n−1)×2xy}= 2n ×2{(x−y) 2 +(n−1)xy}=n{(x−y) 2 +(n−1)xy} |
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