that (An) rges in babilit to A II ntains a further subsequence that converges a.e. to X. only if every subseque

Q: Σ > lan| < o, (-1, 1] For prove that 2 anx" converges uniformly on n=0 EM:

A: The proof for the convergence on [-1, 1] is shown below.

Q: Let fn RR be a sequence of continuous functions which converg uniformly to a function f : R → R. Let…

A: see my solution

Q: Let x be an accumulation point of {an|n ∈ N}. Prove that there exists a subsequence of {an} ∞ n=1…

A: We need to show that there is a subsequence which converges to x

Q: 6. Use e 6 delinition and prove that he soquence, baving general term converges to 3.

A:

Q: =1 nº+1

A:

Q: if -Why does sin(an) Converge is Ano and an converges

A: Apply Mean Value Theorem on f(x)=sin(x) in the interval [0,x] ,    x&gt;0.  So, f'(x)=cosx. By Mean…

Q: 4 o n In n In (In n )[ In (In (In n ))] is convergent or 3. Determine whether divergent.

A: Given:

Q: Suppose that the sequence of functions {fn} and the function f are integrable on [a, b] and that…

A: Given that,  The functions fn and f are integrable on a,b. fn converges to f on uniformly a,b. an…

Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: 7. Prove that a converges if kak→ 0 as k→ ∞ for some > 1. Does the result hold if a = 1?

A: The objective of the question is to prove that a sequence converges if the absolute value of its…

Q: 00 Let r be a constant. Suppose ' converges to -1, then the sum of )r' is i-1 i-0

A:

Q: Let Xn=cos пл 2 then limit supremum of the sequence is

A:

Q: In(1+2e") d) an n

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: (-1)* k4/3 k=1 a) Converges both absolutely and conditionally b) Converges conditionally c)…

A:

Q: SELECT (n!)? (2n)! .()* B) is similar to G A) converges C) is similar to )" D) diverges

A: We will use Ratio Test to determine convergency

Q: Show if the following question converge or diverges

A:

Q: be a sequence of F-integrable functions on [a, t ow f is F-integrable and

A: Let  be a sequence of integrable functions whose choose  are arbitrary.Since  is uniformly…