So for the formula $\dfrac {1}{x}$, If you were to add up all $y$ values from $x=1$ to $x=∞$, wouldn't the sum approach a number because even though you are always adding, aren't you just adding smaller and smaller numbers? Wouldn't this mean that it approached a certain number?
Why does $1/x$ diverge?
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calculus
sequences-and-series
integration
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2The integral or the sum? – 2010-09-21
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1To elaborate on Qiaochu's comment: while the series you describe in your actual posting is obviously related to the function in the topic, they are actually quite different things. You should probably revise the topic. – 2010-09-21
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1$\frac1x$ converges to $0$ as $x\to\infty$. The OP probably won't see this comment anyway, as they have not logged in recently. The posted answers are correct, and another way to illustrate that the above reasoning (posted in the question) is not, is to consider $\frac{1+x}x$ instead. Again we are "adding smaller and smaller numbers", but each of them is bigger than $1$. – 2016-02-18
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0Can anyone give a geometric demonstration of this series? – 2017-03-20