InterviewSolution
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InterviewSolution
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The sequence `{x_(k)}` is defined by `x_(k+1)=x_(k)^(2)+x_(k)` and `x_(1)=(1)/(2)`. Then `[(1)/(x_(1)+1)+(1)/(x_(2)+1)+...+(1)/(x_(100)+1)]` (where `[.]` denotes the greatest integer function) is equal toA. `0`B. `2`C. `4`D. `1` |
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Answer» Correct Answer - D `(d)` `(1)/(x_(k+1))=(1)/(x_(k)(x_(k)+1))=(1)/(x_(k))-(1)/(x_(k)+1)` `implies(1)/(x_(k)+1)=(1)/(x_(k))-(1)/(x_(k-1))` `:. (1)/(x_(1)+1)+(1)/(x_(2)+1)+...+(1)/(x_(100)+1)=(1)/(x_(1))=(1)/(x_(101))` As `0 lt (1)/(x_(101)) lt 1` `:.[(1)/(x_(1)+1)+(1)/(x_(2)+1)+...+(1)/(x_(100)+1)]=1` |
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