Recent content by gregy6196

Help!

yh ur right, but how would i approach this

the hint doesn't make sense to me and i think it is ussing epsilon-delta

Homework Statement prove that if k>1 then kn→∞ an n→∞ there is a hint given. (hint:let k=1+t where t>0 and use the fact that (1+t)n>1+nt) (ii) prove that if 0<k<1 then kn→0 as n→∞ Homework Equations The Attempt at a Solution if k>1 then kn+1-kn=kn(k-1) (ii) 1/k>1 then1/kn→∞

For all n

what would be the first term?

Homework Statement Give an example of a sequence {an}, satisfying the following: {an} is monotonic 0<an<1 for all n and no two terms are the same lim(n→∞) an = 1/2 Homework Equations what is monotonic The Attempt at a Solution 1/(2√n) n/(2n-1) 1/2^n just been trying...

thanks for this, can you please give a counter example to show the converse is false?

thanks. can you please show me how to approach it

i can prove it graphically but i don't know the deffinitions and this is not for assingnment, once someone shows me how its done then i can start my assignments, i need the basics first

Explain why this is no good as a definition of continuity at a point a (either by giving an example of a continuous function that does not satisfy the definition or a discontinuous one that does): Given ε > 0 there exists a \delta > 0 such that |x – a| < \epsilon \Rightarrow |f(x) – f(a)| <...

if lim(n→∞) an = ∞ then prove lim(n→∞) 1/an = 0 is what it shoud say say sorry. where an is a sequence

if lim(n→∞)an=0 then prove lim(n→∞)1/an=0 how do i do this, i know how to proove it geometrically, but how do you write the proof using ε and \delta Give a counter example to show that the converse is false.