Thread: Convergence Sequence (Analysis)

Hi, im not sure if this is in calculus or number theory section...

Using the definition of a convergent sequence show that converges to zero.

Thanks in advance!!
-ynot-

Originally Posted by ynotidas

Hi, im not sure if this is in calculus or number theory section...

Using the definition of a convergent sequence show that converges to zero.

Thanks in advance!!
-ynot-

Big Hint: multiply by the conjugate over itself and simplify. of course, you have to do this within the framework of the definition

Thanks!!
i got to



i have no idea what to do next??

Originally Posted by ynotidas

Thanks!!
i got to



i have no idea what to do next??

ok, another hint:



now see if you can finish up. look at the definition of convergence to see what you have to show

thanks, do i do this?



then n>1/(4epsilon^2)

thus |An - 0| < epsilon if n>1 & n>1/(4epsilon^2)

n*> max{1,1/(4epsilon^2)}

n>=n*, we have |An-0|<epsilon

[SORRY it's taking me forever to type it in the [math} mode]

Originally Posted by ynotidas

thanks, do i do this?



then n>1/(4epsilon^2)

thus |An - 0| < epsilon if n>1 & n>1/(4epsilon^2)

n*> max{1,1/(4epsilon^2)}

n>=n*, we have |An-0|<epsilon

[SORRY it's taking me forever to type it in the [math} mode]

you want to show that

For every , there exists an , such that implies



So let and choose such that

Then blah blah blah

QED