InterviewSolution
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InterviewSolution
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If `Delta_(r) = |(1,r,2^(r)),(2,n,n^(2)),(n,(n(n_1))/(2),2^(n+1))|`, then the value of `sum_(r=1)^(n) Delta_(r)` isA. nB. 2nC. `-2n`D. `n^(2)` |
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Answer» Correct Answer - C We have, `underset(r=1)overset(n)sum Delta_(r) = |(underset(r =1)overset(n)sum 1,underset(r=1)overset(n)sumr,underset(r =1)overset(n)sum 2^(r)),(2,n,n^(2)),(n,(n(n+1))/(2),2^(n+1))|` `rArr underset(r =1)overset(n)sum Delta_(r) = |(n,(n(n+1))/(2),2^(n +1)-2),(2,(n(n+1))/(2),2^(n+1)),(n,(n (n +1))/(2),2^(n+1) -2)|` `rArr underset(r=1)overset(n)sum Delta_(r) = |(n,(n(n+1))/(2),2^(n+1) -2),(2,n,n^(2)),(0,0,2)| ["Applying " R_(3) rarr R_(3) - R_(1)]` `rArr underset(r=1)overset(n) sum Delta_(r) = 2 {n^(2) - n (n +1)} = -2n` |
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