InterviewSolution
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InterviewSolution
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The numbers `1,3,6,10,15,21,28."……"` are called triangular numbers. Let `t_(n)` denotes the `n^(th)` triangular number such that `t_(n)=t_(n-1)+n,AA n ge 2`. The number of positive integers lying between `t_(100)` and `t_(101)` areA. 99B. 100C. 101D. 102 |
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Answer» Correct Answer - B Given sequece `1,3,6,10,15,21,28,"…"` where `t_(n)=t_(n-1)+n,AA n ge 2` So, `t_(n)=[t_(n-2)+(n-1)]+n` `vdots " "vdots " " vdots " "` `t_(n)=t_(1)+2+3+"........"+(n-1)+n` `t_(n)=1+2+3+"......"+n` `t_(n)=(n(n+1))/(2)` `t_(100)=(100xx101)/(2)=5050` `t_(101)=(101xx102)/(2)=101xx51=5151` Number of positive integers lying between `t_(100)` and `t_(101)` `=5151-5050-1` `=101-1=100`. |
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