Recent content by rohitmishra

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    Is the Sequence s_n Bounded and Monotone If x_n Is Bounded and Monotone?

    Let (xn) be a seq of real nos and let sn = x1+x2+x3+...+xn / n. prove that if if xn is bounded and monotone, then sn is also bdd and monotone. How can i got about this one.. ? I got it in the test today and i couldn't figure it out. only hint i could think of is how do i prove if xn...
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    Can You Prove Lim(x->0) g(x) Equals L When g(x)=f(ax)?

    Suppose f:R->R , Lim (x->0) f(x) = L. and a>0. Define g:R->R by g(x)= f(ax). Prove that Lim (x->0) g(x) = L ? My Solution. I am not able to prove it as equal to L. From what I get it is Lim (x->0) g(x) Lim (x->0) a * f(x) a* Lim (x->0) f(x) a* L = aL ?? I have to...
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    Graduate Proving Cauchy Sequences using the Definition

    How would you guys go about this one If 0<r<1 and |x(n+1) - x(n)| < r ^n for all n. Show that x(n) is Cauchy sequence.
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    Real Analysis: Proving Lim(yn)=0 from Lim(xn)=Infinity & Lim(xnyn)=L

    Can you help me how i can construct the proof.. ? I understand what you meant. But, How can I assume my yn is 1/xn ?
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    Real Analysis: Proving Lim(yn)=0 from Lim(xn)=Infinity & Lim(xnyn)=L

    limn->∞ 1/xn = 0
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    Real Analysis: Proving Lim(yn)=0 from Lim(xn)=Infinity & Lim(xnyn)=L

    I have lim(xnyn) =L. How can I start of a prove assuming two sequences That is x(n) = 2x(n) which wud tend to infinity and Lim (yn) = 1/x(n) = 0. Can you tell me what the Hypothesis wud be ?
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    Real Analysis: Proving Lim(yn)=0 from Lim(xn)=Infinity & Lim(xnyn)=L

    Question : Let (xn) and (yn) be sequences of real numbers such that lim(xn)= infinity and lim(xnyn)=L for some real number L. Prove Lim(yn)=0. I've been trying to solve this question for a long time now. I've no success yet. Can anyone guide me as to how i can approach it.