1112-22+32-42............... (2n)2
This question was from the test. I did not understand the solution. Could someone tell me the solution again?
1<sup>2</sup>-2<sup>2</sup>+3<sup>2</sup>-4<sup>2</sup>......... n<sup>2</sup>
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4 Answers
11The minute and hour hands of the clock meet at 12 o'clock
What is the next time they meet?
62The first question is given on our tests. I dont remember the test number. But I think it had n=100.
But the answer is very simple.
Try to take
12-22 = (1-2)(1+2) = -(1+2)
32-42 = (3-4)(3+4) = -(3+4)
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(2n-1)2-(2n)2 = (2n-1-2n)(2n-1+2n) = - (2n-1 + 2n)
Taking summation of all we get sum
= -(1+2) - (3+4) - (2n-1 + 2n)
= - (1+2+3+.... 2n) = -2n(2n+1)/2 = -n(2n+1)
I hope this is clear now!