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1 2 -2 2 +3 2 -4 2 +5 2-.............. is 1)n(n+1)/2 2)-n(n+1)/2 3)-n(n+2)/2

12-22+32-42+52-..............
is
 
1)n(n+1)/2
2)-n(n+1)/2
3)-n(n+2)/2

Grade:11

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
Using the identity, (a2-b2) = (a+b) * (a-b), we can write the given sequence as (assuming that the sequence has n terms) -
(1+2)(1-2) + (3+4)(3-4) + (5+6)(5-6) …....... + ((n-1)+n)((n-1)-n)
= -1(1+2) + -1(3+4) + ….... + -1(n+n-1)
= -1(1+2+3+.......+n-1+n)
And the term in the bracket is the sum of 1stn natural numbers, and so we can write it as -
= -n(n+1)/2

Thus the answer is option 2.

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