2n + 3 2n+3 Let 2 4" and an n=1 an+1 a) Find lim n+ 00| Un 2n+3 b) Determine whether 2 is convergent or 4" n =1 divergent (show all your works)

Q: 2t2X+ -1 14x2 DAna lim X-7-1 FCx) X-フー1- (-1) 2+21-)) - 2 + 1 ext O And lim 7-1t Lim X-7-1 -1+1 -…

A: Consider the given function,

Q: 1. Let f be a continuous function, and define a sequence by a₁ = a, an+1 = f(an). This is called an…

A: Advance maths

Q: {xn}1 such that inf(7) 25. Give an example of a sequence of real numbers 7 0, lim inf(7) = 1, lim…

A:

Q: find either lim 5x3 x→∞ ex one that takes less time!) Find lim (1 +5)* X→∞ 5x3 x→0 ex-1 or lim using…

A: As per the rules we are supposed to answer the first question and rest can be reposted.

Q: 3-1t 4.) Iim 5x-4メト! 入ーレ Atuメ-X 5) メー3 メー0 2入+ (4x

A: NOTE: Refresh your page if you can't see any equations. . divide by x2

Q: ∑(sqrt(n+1) - sqrt(n))/sqrt(n2+n) does it converge or diverge? (show each step please)

A:

Q: If the sequence (xn) convergence to x, then the sequence (Vxn) also .x convergence to

A:

Q: Let {bn} be a sequence whose limit is 3. Show that if B is an upper bound of this sequence, then 3 <…

A: We will use the definition of limit.

Q: Determine whether the sequence is monotonic and whether it is bounded. sinyn an

A: It is required to check whether the given sequence is monotonic and bounded.

Q: 3x + 2x + x+ 1 Let Ax) = What types of asymptotes does Ax) have? Explain. .2 x* +x-2

A: To find the asymptotes of f(x).

Q: Which of these is (are) always VALID : (a) If an is divergent, then lim an 70. (b) If an is…

A: we will solve this by using counter examples

Q: 8+x-4x? Lim\ belowr → 0∞ V6+x²+7x* O a. -4/7 O b. 4/7 O c. 4//7 O d. -4/7

A:

Q: (-9)"+1 Let an 10n Determine whether the sequence {an} is convergent or divergent. If it is…

A: an=(-9)n+110n A sequence is convergent if value of limit is define and finite as n approaches to…

Q: Determine whether the sequence {(3" + 5")/"} is convergent or not.

A:

Q: Let (Xn) be convergent seq in R show that (IXnl) is convergent and that lim | Xn] = | X | n

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Q: limitn->infinity (sprt(n+1)) -(sqrt(n+2))

A: Calculate the limit:  limn→∞n+1-n+2=limn→∞n+1-n+2·n+1-n+2n+1+n+2…

Q: x? — х -2 lim 2 x +3x + 2 X→-1 X

A: First we factories then take limit.

Q: or converges

A:

Q: finding Ⓡ a se lim, soo Jn. = JA n

A: given

Q: How did you get the (2n+1)(2n-1)? I just don't know where the (2n+1) came from. thanks in advance

A: use the general principle of mathematical induction.

Q: 3n · (2n)! br Determine lim bn 2(2n + 1)! n→∞

A:

Q: using proof of contradiction show that if n is any odd number and m is any even integer then 3^(n^3)…

A: Let n be any odd number and m be any even integer. To show 3n3+2m2 is odd. Suppose not. Then 3n3+2m2…

Q: If limkoo ak 0 then Eak is convergent.

A:

Q: Let (rn) be a bounded sequence of real numbers from [1/10, ∞) (that is, each entry rn is ≥ 1/10),…

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Q: Only use epsilon defination , Let be a sequence of positive terms such that pn-> p show that…

A: We apply only Epsilone defination.

Q: Show that a strictly decreasing sequence with a convergent subsequence is convergent. (Advanced…

A: Let un be a monotonically decreasing sequence. urn be a subsequence of un such that lim urn=l Since…

Q: 3n³-4n+1 Find lim,00 . (show all necessary en details)

A: Limits are used to calculate the approaching value of the function at which the exact value of the…

Q: 7n+2 lim no 8n + 100 = NIN

A:

Q: lim n->infinty ((4n+4)(4n+3)(4n+2)(4n+1))/((n+1)4 3964)

A: Divide by n^4 in denominator and numerator