InterviewSolution
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InterviewSolution
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The sum of series `sec^(-1)sqrt(2)+sec^(-1)(sqrt(10))/3+sec^(-1)(sqrt(50))/7++sec^(-1)sqrt(((n^2+1)(n^2-2n+2))/((n^2-n+1)^2))`is`tan^(-1)1`(b) `n``tan^(-1)(n+1)`(d) `tan^(-1)(n-1)`A. `tan^(-1) 1`B. `tan^(-1) n`C. `tan^(-1) (n + 1)`D. `tan^(-1) (n -1)` |
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Answer» Correct Answer - B `T_(n) = "sec"^(-1) sqrt(((n^(2) +1) (n^(2) -2n + 2))/((n^(2) -n +1)^(2)))` `rArr sec^(2) T_(n) = ((n^(2) + 1) (n^(2) -2n + 2))/((n^(2) -n + 1)^(2))` `rArr sec^(2) T_(n) = ((n^(2) +1)^(2) + (n^(2) +1) -2n(n^(2) + 1))/((n^(2) - n+ 1)^(2))` `rArr sec^(2) T_(n) = (1 + (n^(2) + 1 -n)^(2))/((n^(2) -n + 1)^(2))` `rArr tan T_(n) = (1)/(n^(2) -n + 1)` `rArr tan T_(n) = (n -(n -1))/(1 + n(n -1)) = tan^(-1) n - tan^(-1) (n -1)` `:. S = T_(1) + T_(2) + T_(3) +..+ T_(n)` `:. S = tan^(-1) n` |
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