/sci/ - Science & Math

No sadly

[math] x(n)=\sum_{k=1}^n 9\cdot 10^{2-k} [/math]

>>9259671
Take your favourite convergent series and multiply every term by 100 divided by the original limit of that series.

>>9259671
[math]x(n)=100[/math]

>>9259691
wow holy shit BTFO

>>9259691
What if my favourite convergent series is
[eqn] \sum_{k=0}^\infty \left( \frac{k+1}{k^2 + 2k + 2} - \frac{k}{k^2 + 1} \right) [/eqn]
?

>>9259721
[math]\sum_{k=0}^\infty 100\left( \frac{\frac{k+1}{k^2 + 2k + 2} - \frac{k}{k^2 + 1}}{ \sum_{k=0}^\infty \left( \frac{k+1}{k^2 + 2k + 2} - \frac{k}{k^2 + 1} \right)}\right)[/math]

>>9259721
God damn it

>>9259671
[eqn] \frac{600}{\pi^2} \sum_{n=1}^\infty \frac{1}{n^2} [/eqn]

>>9259691
[math] 100\sum_k\left(\frac{0}{\sum_{k=1}^{\infty}0}\right) [/math]

>>9259768
If your favourite series is [math]\sum_{k=0}^\infty 0[/math], you deserve what you get.

>all these sub-70 IQ overcomplicating shit
[eqn]\sum_{n\,\geqslant\,0} 100\,\delta_{n,\,0}[/eqn]

>>9259692
gg ez

>>9259671
[math]\alpha\sum_{n=1}^\infty a_n[/math]
where (a_n) is a convergent series and alpha is a scalar that sets the limit to 100.

>>9259671
Not anymore. It commited suicide a month ago.

>>9259671
(1/n) + 100

or simply

100

>>9260065
>series

>>9260085
Yes 100 + 0 + 0...
A little less trivial? 99+.9 +.09 +.009...

>>9260085
What are constant series?

choose a sequence [math](a_n)[/math] such that [math]\sum_n a_n\to \ell\in\mathbf{R}\setminus\{0\}[/math].
then [math]\frac{100}{\ell}\sum_n a_n\to 100[/math].

>>9260118
divergent for all non-zero constants

>>9259671

100 followed by infinite zeros

>>9260124
I mixed up sequences and series.

>>9259671
[math]\displaystyle
-1200\times\sum_{n=1}^{\infty} n
[/math]

>>9259671
yes, [math]\sum_{k=1}^\infty \frac{(-1)^{k+1}}{k}[/math] under some rearrangement of terms

>>9259671
>is there a convergent series which has a limit of 100
The existence of a real number is equivalent to the existence of an infinite amount of series of rational numbers converging against it.
Yes.

>>9259671
p-series

anything ^n fraction if int is >1 it converges

Of course there is. There are many ways of proving it
the simplest is that you can make a series out of every sequence by summing differences of the terms…
the most fun way is with the Riemann theorem :
https://en.wikipedia.org/wiki/Riemann_series_theorem

>>9259688
glorious

>>9259671
Let [math](a_n)_{n\in\mathbb{N}}[/math] be a real sequence defined by
[eqn]a_n = \begin{cases}100 &\text{if $n = 0$}\\ 0 & \text{otherwise}\end{cases}[/eqn]

Then the series
[eqn]\sum_{k=0}^\infty a_n[/eqn]
is convergent with limit 100.

>>9259671
ah yes, the series [math]x_1 = 100, x_n = 0 \forall n>1[/math]
how interesting...

>>9260139
how about infinite zeros followed by 100

>>9259691
My favourite convergent series is 0,0,0, ...

>>9259671
How to calculate factorial of real numbers (example 0.5 and sqr(2))? Explain pls or give me literature so I can do it myself

>>9263600

Sounds good to me

>>9263634
Gamma function