Show that a, converges to A iff {a, - A) converges to 0.

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: Use the root test to determine whether >a, converges, where An is as follows. n=1 332. a, = n/ e"

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Q: Show the following statement is true or not with proof. If {n} converges then {[sn]} converges.

A: We have to show the following statement is true or not with proof. If {sn} converges then {|sn|}…

Q: Prove that or quari -1+ X.- ズい 2. X. ntl converged number Ja to 2.

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Q: For each nЄ Z+ let fn : R → R be the function пх fn(2) n|x| +1° (a) Prove that (fn) converges…

A: Given the sequence of functions  defined by .(a)Consider the limit,This is true for every 0≠x∈R.…

Q: Let (an). (bn) be two bounded sequences. a. Show that lim sup max(a,, b,) > max(lim sup an, lim sup…

A: Given: Let's say there are two bounded sequences (an, bn) .a. Demonstrate that limn→∞sup max(an,…

Q: Determine i absolutely conergent, condifionelly oliverpent. (Do not use the followige serres i's…

A: Don't worry, we will make use of the Comparison test. If the sum of |a[n]| converges, then the sum…

Q: Suppose that dz converges. What can we conclude about the constant p? Op>1 Op Op< 3

A: Explanation of the answer is as follows

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

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Q: 5. Let an be recursively defined by ao = Show that an converges, and find its limit. 1/2, an+1 =…

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Q: 9. Prove that if {fn(x)} converges uniformly to the function f(x) on each of the sets A1, A2, ...,…

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Q: an2

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Q: ,(-1)" converges conditionally, but not absolutely. Show all work. 3n Prove E

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Q: exercise 1.5. Let n > 1. Prove that 6"+1 + 7"+1 6" + 7" is reduced.

A: When a mathematical statement is given to be proved for a subset of natural numbers, we use the…

Q: Construct a sequence of unbounded functions 9n : [0,1] → R that converges pointwise to a bounded…

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Q: Σ converges/diverges N! 9) Show that

A: Ratio test