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Omni-MATH / Let t_(n) equal the integer closest to √(n). What is the sum (1)/(t₁)+(1)/(t₂)+(1)/(t₃)+(1)/(t₄)+⋯+(1)/(t₂₀₀₈)+(1)/(t₂₀₀₉)+(1)/(t₂₀₁₀)?

Problem

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problem

Let tnt_{n} equal the integer closest to n\sqrt{n}. What is the sum 1t1+1t2+1t3+1t4+⋯+1t2008+1t2009+1t2010\frac{1}{t_{1}}+\frac{1}{t_{2}}+\frac{1}{t_{3}}+\frac{1}{t_{4}}+\cdots+\frac{1}{t_{2008}}+\frac{1}{t_{2009}}+\frac{1}{t_{2010}}?
Plain-text mathematical notation (without MathML)
Let t_(n) equal the integer closest to √(n). What is the sum (1)/(t₁)+(1)/(t₂)+(1)/(t₃)+(1)/(t₄)+⋯+(1)/(t₂₀₀₈)+(1)/(t₂₀₀₉)+(1)/(t₂₀₁₀)?
Original LaTeX notation
Let $t_{n}$ equal the integer closest to $\sqrt{n}$. What is the sum $\frac{1}{t_{1}}+\frac{1}{t_{2}}+\frac{1}{t_{3}}+\frac{1}{t_{4}}+\cdots+\frac{1}{t_{2008}}+\frac{1}{t_{2009}}+\frac{1}{t_{2010}}$?

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Source and history

task_id
9668917f-0286-551a-9ae4-32d3cf0845c8
task_key
test--9668917f-0286-551a-9ae4-32d3cf0845c8
task_revision_id
1
config / split
/ test

Official source

initial import