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Real Analysis
Given that f is the real valued function defined by f(x) = 1 / (1 + e^x). And I = (1/4, 1/2). We define the sequence (Un) by Uo = 1/4 and for all n E N where N = set of natural numbers, and E represents "an element of", U(n +1) = f(Un).
(i)Show that Un E I.
(ii) Show that for all n E N, we have ㅣU(n+1) - sㅣ <= 1/4ㅣUn - sㅣ Where s Eb(1/4, 1/2)
(i)Show that Un E I.
(ii) Show that for all n E N, we have ㅣU(n+1) - sㅣ <= 1/4ㅣUn - sㅣ Where s Eb(1/4, 1/2)
Real Analysis
show that the series 1 - 1/2³ + 1/3³ - 1/4³ + 1/5³ - .... is absolutely convergent
Real Analysis
if a sequence ⟨Sn⟩ is defined by Sn = Sn/1-Sn-1, s>0, s1>0. then show that the sequence converges to the positive root of the equation x²+x-5=0
Real Analysis
find rational number r=m/n . Such that √5 < r < √6
Real Analysis
Is the following statements True or False? Please state your answer and explain them.
1) If a < L for every element in a set A, then sup A < L.
2) limit of (an) when n goest to infinity is L if and only if the limit of |an - L| when n goes to infinity is 0.
1) If a < L for every element in a set A, then sup A < L.
2) limit of (an) when n goest to infinity is L if and only if the limit of |an - L| when n goes to infinity is 0.
Real Analysis
find the laplace transform of (e^-at -e^-bt)/t
Real Analysis
If A={x∈Q,x<3} then find Sup(A)
Real Analysis
If (an)infinityn=1 is a sequence of real numbers satisfying an+12 =2an-1, then,
limn->infinity an = ?
Real Analysis
Discuss order-completeness of the set of rational numbers
Real Analysis
Consider the following sequence of successive numbers of the 2^k-th power: 1, 2^2^k, 3^2^k, 4^2^k, 5^2^k, … Show that the difference between the numbers in this sequence is odd for all k ∈ N?
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#340153 on Dec 2023
#340153 on Dec 2023