Not always true. Eg the divergent series 1,0,2,0,3,0,4,... has both convergent and divergent sub-sequences.
true
yes
true
yes
Every convergent sequence is Cauchy. Every Cauchy sequence in Rk is convergent, but this is not true in general, for example within S= {x:x€R, x>0} the Cauchy sequence (1/n) has no limit in s since 0 is not a member of S.
no converse is not true
iceland true fact
For the statement "convergence implies boundedness," the converse statement would be "boundedness implies convergence."So, we are asking if "boundedness implies convergence" is a true statement.Pf//By way of contradiction, "boundedness implies convergence" is false.Let the sequence (Xn) be defined asXn = 1 if n is even andXn = 0 if n is odd.So, (Xn) = {X1,X2,X3,X4,X5,X6...} = {0,1,0,1,0,1,...}Note that this is a divergent sequence.Also note that for all n, -1 < Xn < 2Therefore, the sequence (Xn) is bounded above by 2 and below by -1.As we can see, we have a bounded function that is divergent. Therefore, by way of contradiction, we have proven the converse false.Q.E.D.
True. Oceanic lithosphere is created at divergent boundaries where tectonic plates move away from each other. Magma rises from the mantle to fill the gap and solidifies to form new oceanic crust.
is where two plates pull away from each other
false
True
true
yes
Yes.
yes
true