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

Question

Riddhish Bhalodia · Answer

Using the identity, (a 2 -b 2 ) = (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) &hellip;....... + ((n-1)+n)((n-1)-n) = -1(1+2) + -1(3+4) + &hellip;.... + -1(n+n-1) = -1(1+2+3+.......+n-1+n) And the term in the bracket is the sum of 1 st n natural numbers, and so we can write it as - = -n(n+1)/2 Thus the answer is option 2.

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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+5^{2-..............}
^is

^1)n(n+1)/2
^2)-n(n+1)/2
^3)-n(n+2)/2

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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)/22)-n(n+1)/23)-n(n+2)/2

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1²-2²+3²-4²+5^{2-..............}
^is

^1)n(n+1)/2
^2)-n(n+1)/2
^3)-n(n+2)/2