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Let a<b let X1=a and X2=b and
Xn+2 = Xn+1 /2 +Xn/2 in another way Xn+2 = Xn+1 +Xn all over 2
Follow these steps to show that Xn Cauchy
1) Draw picture and let L=b-a
2) Use induction to show that absolute value l xn+1 xnl = L/2^(n-1)
3) Conclude that sequence Xn is Cauchy
Find a Cauchy sequence in (0,1) that does not converge to a point of (0.1)
ok just any answers to the first question?
What is the set of accumulation points of the irrational numbers?
Give an example of abounded set of real number with exactly three accumulation points?
Let A subset of R A ⊊ R and let x in R show that x is an accumulation point of A if and only if there exists of a sequence of distinct points in A that converge to x?
any help will be extremely appreciated
thank you bobbym i really appreciate this
and i'm still waiting for second question can any one solve it in this forum
and that will be greatly appreciated
xn = 1, 1/2,1/3,.........sum ∑1/n
show that xn is monotone but not converge
let
0<xn<7 fore each n by bolzano theorem B-W
xn has convergent sub sequence in what interval the limit of this sequence lie?
find convergent sequence in (0,1) that dosnot converge to a point in (0,1]
give example
Xn is bounded sequence and Yn is convergent sequence but XnYn doesnot converge
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