What's the slowest growing divergent infinite sum, if there

>>7935382
... 1/(2x)?

nice pic

>>7935394
That grows at the same rate
1/(2X) = O(1/x)

I want a function f(x) that has a diverging infinite sum but f(x)=o(1/x)

>>7935394
rekt

Can somebody explain this to me?

>>7935406
Either I didn't phrase it right in the OP or you guys don't understand growth rate

>>7935405
.5/2x

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>>7935412
This is an infinite sum of 1/x. This sum doesn't actually have a value because it diverges to infinity. However, 1/x is a very slow growing function. I was wondering if there are any functions with an even smaller growth rate that also still have a divergent infinite sum.

For example, 1/(x^2) has a slower growth rate, but the sum of the infinite series converges to a finite number.

Also, notice that 1/(2x) and 1/x both have the same growth rate because the ratio between the two functions as x approaches infinity is a constant, not 0 or infinity.

>>7935413
1/(n*log(n))

1/(n*log(log(n)))

Just guesses. Might want to test.

>>7935419
If f(x)/g(x) is a constant as x approaches infinity, the two functions have equal growth rates, you baiting dumbass

>>7935423
this clearly grows faster

>>7935421
log(x)/x probably or shit like that. this isn't an interesting question

>>7935426
disregard this, I suck cocks

>>7935424
You asked for "slower growing". Just because the O(..) is the same doesn't make him wrong with respect to your question, which is first-page-of-googleable, you lazy dumbass.

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>>7935423
Yeah, you're right, it does diverge while having a smaller growth rate!

>>7935430
>b...but .5/2x wasn't b8
Jesus anon, don't try to justify that

>>7935431
... Why n=4? That's going to bother me.

>>7935442
Something to do with series condensation or something, I didn't watch the whole video

https://www.coursera.org/learn/advanced-calculus/lecture/0ssbL/does-sum-1-n-log-n-converge

>>7935442
The starting n value is arbitrary. You'll get the same results assuming n is a non-zero natural number.

>>7935447
Which is why it bothered me that n!=1. Makes it seem like something less than 4 might not diverge.

>>7935421
I'm pretty sure that sums to -12 actually

>>7935475
If n=1 the logarithm is 0.

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>>7935480
Well-memed, friendo