# Thread: how does this series behave..

1. ## how does this series behave..

i was tought this trick to make series converge to 0
for example
f_n (x) =1 ,when x belongs to [n,(n+1)]
f_n (x) =0 when it doesnt
so no matter what x value we have
when n goes to infinity the value 1 section will "run away
and it always converge to 0

now i cant undestand if the following function is a such a function.
f_n(x)=(n)^0.5 ,when x belongs to [0,1/n]
f_n(x)=0 ,when it doesnt

herewhen n goes to infinty
i dont have a moving section like before

here the section shrinks
and static am i correct?

2. Originally Posted by transgalactic
i was tought this trick to make series converge to 0
for example
f_n (x) =1 ,when x belongs to [n,(n+1)]
f_n (x) =0 when it doesnt
so no matter what x value we have
when n goes to infinity the value 1 section will "run away
and it always converge to 0

now i cant undestand if the following function is a such a function.
f_n(x)=(n)^0.5 ,when x belongs to [0,1/n]
f_n(x)=0 ,when it doesnt

herewhen n goes to infinty
i dont have a moving section like before

here the section shrinks
and static am i correct?
But you do have a moving section. Given any positive number $x$ the Archimedean principle furnishes us with a $N\in \mathbb{N}$ such that $\frac{1}{N} thus for $N \le n\implies f_n(x)=0$. Thus for any positive $x$ we can see that $\lim_{n\to\infty}f_n(x)=0$.

3. i cant understand how its moving as n goes to infinty

what you said is just that it has a value of 0
but i think that its because the section moving
but because the section is static but shrinks till zero

for n=2
0<x<1/2

for n=100
0<x<1/100
am i correct?

4. Originally Posted by transgalactic
i cant understand how its moving as n goes to infinty

what you said is just that it has a value of 0
but i think that its because the section moving
but because the section is static but shrinks till zero

for n=2
0<x<1/2

for n=100
0<x<1/100
am i correct?
I haven't the slightest idea of what you mean. Given any positive $x$ by the Archimedean principle I know that eventually $\frac{1}{n}.

5. imagy a graph of that function

6. Perhaps the validation of another member will convince you. Maybe I am, in fact, wrong. In which case another member will chide me and we can move on.