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Omni-MATH / A sequence of numbers t₁,t₂,t₃,… has its terms defined by t_(n)=(1)/(n)−(1)/(n+2) for every integer n≥1. What is the largest positive integer k for which the sum of the first k ter…

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problem

A sequence of numbers t1,t2,t3,…t_{1}, t_{2}, t_{3}, \ldots has its terms defined by tn=1n−1n+2t_{n}=\frac{1}{n}-\frac{1}{n+2} for every integer n≥1n \geq 1. What is the largest positive integer kk for which the sum of the first kk terms is less than 1.499?
Plain-text mathematical notation (without MathML)
A sequence of numbers t₁,t₂,t₃,… has its terms defined by t_(n)=(1)/(n)−(1)/(n+2) for every integer n≥1. What is the largest positive integer k for which the sum of the first k terms is less than 1.499?
Original LaTeX notation
A sequence of numbers $t_{1}, t_{2}, t_{3}, \ldots$ has its terms defined by $t_{n}=\frac{1}{n}-\frac{1}{n+2}$ for every integer $n \geq 1$. What is the largest positive integer $k$ for which the sum of the first $k$ terms is less than 1.499?

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Source and history

task_id
1a422da4-7320-5362-a4f2-2420cc701cba
task_key
test--1a422da4-7320-5362-a4f2-2420cc701cba
task_revision_id
1
config / split
/ test

Official source

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