What's the slowest growing divergent infinite sum, if there even is one at all?
The slowest I can think of is 1/x.
>>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
>>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
>>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.
>>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.
>>7935480
Well-memed, friendo
