3|n(n+ 1)(n+ 2), Vn E N

Q: >k = 1 + 2 + 3 + · · · + n = ... k= n (п + 1) (b) (а) п! 2 п (п + 1) (2n + 1) (d) (с) nk

A:

Q: )"-( 18 6. lim V n4n +(4n)" 2+ n2 4 4+ n2

A:

Q: x(n) = (0.8)" u(-n-1)

A: Topic:- calculus

Q: n2 + 40 9. n2 + 3n +1 { Sn=1

A: We have to check sequence is increasing or decreasing, monotonic, bounded above or below or bounded:

Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

A:

Q: 3Fn - F n-2= Fn+2 for n>3

A:

Q: n=0 2n 18. n=0 V4 + n2 8

A:

Q: (-2)"+1 n+ 5" (2n)! 2n - n! - n (a) (b) (-1)". n=1 n=1 (c) E(-1)": (n!)'3" (2n + 1)! (d) 5 (-1)"…

A:

Q: If (ar + br) 4n and n+1 k-1 E(ak - br) 1 then ar = | n+2 k-1 k-1 3 5. None 2. 72n/2

A: use elimination method Find limit for n tending to infinity.

Q: n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

A:

Q: write down the first five terms of each sequence

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider f(n)=7n+8 and              g(n)= n2 Is f(n) = Ω (g (n))?

A:

Q: (-1)**'n! 1-3-5..(2n+1) n+1

A: The objective is to find whether the series is convergent or divergent.

Q: ( a) Σ-1)t1, n+1 Vn² + 1 n² + 4 n=2 (b) (-1)" n(In n)³ n=2

A:

Q: Identify the two series that are the same.

A: In order identify the same series, just write the few terms of the gives series as follows. (a)…

Q: (-1)n+13n (b) n5n n=1

A:

Q: E(-1)n + 1(n + 8)x" n = 0

A:

Q: 2n [3] (b) E for n 21 2k k=0

A: Answer

Q: Show that n*-n3.5+300n + 234n²log n³ + nVn10 e 0(n*)

A:

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: 1 n +1 k=0 n n(n+1) 2 2 k=0 n 3 E k2 n(n+1)(2n+1) 6 k=0

A: Note: Since you have posted a question with multiple subparts, we will solve the first three…

Q: (c) (-1)". -Tn n=1 n - 1 (d) E(-1)". n3 +1 n=1

A:

Q: 1+n+ Vn n=0 n+ Vn4 + n² +1 O A. 32 O B. 2-8 O C. - 16

A: For checking, whether the series is convergent or divergent, we can directly check the highest power…

Q: -ges 3n +n 9n b) L7-2)n+1n n! n=1 (-10)" d) 242n+1(n+1) n2 (2n – 1)! n=1 0=

A:

Q: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

A:

Q: f(n) = n³, g(n) = 6n + 1 е.

A: Given: e) f(n)=n3 and g(n)=6n+1 To find: a and n0 such that a·f(n)≥g(n)

Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

A: The solution is given as

Q: п d) Σ (-1)" п е n=1 (-1)"*'n² п e) E 2 п +4 n=1 1 Σ- ‚n n=1

A: According to guidelines we can solve only first question. Please submit as separate questions.

Q: 1. Vn + 4 Σ n n=1

A: since you have posted multiple question. I can answer first question as per our company guidelines…

Q: ) = 7- 2x [1, 2] %3D s(n) = 5(n)

A:

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

A:

Q: (2n + 1)(n² + 1) (e) > (n – 1)(n² – 4)² | n=3

A: The given series is divergent.

Q: 4n +1 (a) 2n2 +3 n=0 5n2 – n+1

A: Since multiple questions are asked, I am answering first question

Q: Зп + 1, A) 2n 4 — 2п n=1 n1-3n В) 42n n=0 (-5)1+2n C) 25п-3 n=4

A: Here we apply different tests like comparison test and Leibniz test.

Q: x(n) (0.8)" u(-n-1) -1 1-(0.8)# خيار 3 0 خيار 4 -1 1-(0.8)

A: Solution

Q: Identify the two series that are the same.

A: We have to find which series are same. We have given series…

Q: 4 a. En=1 100 3n3-5n 11 b. nylnn n=1 3n! С. Z1·4·7·10 … (3n + 1) ... n=0 8

A: See the details solution in below

Q: 2 n n Σ (2n – 1 п — 1, =n k k=1

A: we have to prove that                                                we know that…

Q: n Σ k + 2n + n2 | n k=1

A: use the sum of first natural number  to evaluate the sum

Q: (エ+1)n n=D1

A:

Q: e) Un n²-3n+ 1 2n²+1

A: Introduction: A sequence is a collection of functions. This function makes a map from the set of…

Q: true or false. 3Fn > Fn+3 for n = 3

A: Answer is True

Q: (d) (e) n=1 n=1 3n²+ 1 2n² +3 2¹ (n!)² n2(2n!)

A:

Q: 2n 2n E (n"x n:o

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: S (2n)!n² (2n + 2)!

A: We have to find  limn→∞(2n)! n2(2n+2)!

Q: Find the possible values of n. (n2 )" – 2n" + 1 = 0 (n +0,1)

A: We have  n2n-2nn+1=0 and n≠0,1 We can write n2n as n2n=n2n=nn2 So, nn2-2nn+1=0 Let nn=x x2-2x+1=0

Q: 1 Vn > 0, 2(аn+1 — аn) %- 2n

A: Given an=1-12n so an+1=1-12n+1.

Q: 2n ( a ) Ση (v 1 (b) -1)^2?n+13 2n + 1 5n n=1 n=0

A:

Q: 1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

A:

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…