a) 5n + 1 3n2 2" (b) Σ 1 ( c) Σ n=2 nº - 7 - 1 n=1 n=1 3n

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

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Q: In2 + 5n + 4 lim an = 1 %3D %3D 3n2 + 8n + 8 n-00 1n? In2 5n + 4

A:

Q: 2 4 8 n2 + 2n 1 (i) 1 3 (ii) (iii) ) - 9 27 1+ 2n2 ' n=0 2nn n=1

A: Both series we can evaluate using geometric series method.

Q: Determine whether or not the infinite series below converges.

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Given: In(1+ x) (-1)" xn+1 _if |x| < 1 n + 1 n=0 (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of…

A: Solving

Q: 5 4n + 15-n n= 1

A: Given :

Q: 2 6in. 10in E Zin. -

A: find the area of region

Q: ( a ) Ση-1 (b) En=2 n7-1 15n-2 (c) En=1 11n+3 1 (d) Σn1 n14 (-1)" (e) En=1 7n+4

A:

Q: 27. * Σ n(n - 1)anan-2. n=2 + n=0 and

A:

Q: 1 a) Sn+1 = 3 – Sn 25, -35m b) Sn+1 Sn-1 9Sn c) Sn+1 S+1

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: 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: Given: In(1+x) = >) (-1)". -xn+1 if |x| < 1. n+1 n=0 Compute the exact value of -1)"(n+2) 2n+1(n +…

A: Given: ln(1+x)=∑n=0∞(-1)nn+1xn+1 where x&lt;1To Compute: Exact value of ∑n=0∞(-1)n(n+2)2n+1(n+1)

Q: -xx-9 and y=-x+3 у -9-8-7-6-5-4-3 1 y=x: POINT(S): IN 76 NWA -2 N3456789 -2 -3 -6 -7 -8 23456 -9 +2…

A: We have to find the graph

Q: 2n+5,3n | in=0 3n+6 s(0z – z)

A:

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: 2. Find the value of 2n=1 Sn=15 2n + 3.

A:

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: 1 Σ (2n – 3(2n – 1) n=1

A:

Q: Ex : Express the Sum o+ 2+4+6+8 in Sigma nata tion. -2

A:

Q: (-1)"(п + 2) 2n+1(n +1) Compute the exact value of n=0

A: The geometric series formula is ∑n=0∞rn=11-r, where r&lt;1. Simplify the numerator of the given…

Q: 1 (A) E 11 · 12"+1 n=0 12"+1 n=0 (-1)" (B) ), (-1)*+1 . n Σ 6. 7n+1 n=0 7n+1 n=0 1 (C) E (n+1) 6n+1…

A: As per the rule we are doing first three part of the question:   Part (A):

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

A:

Q: a(1 – rª ) n³(1-0.5'g(n) ; (1 – r) (1-0.5) (n³ – n³+0.5!g(n)) 0.5 =(2n3 – – 2n² ) 2 * n³ * 0.5'g(n))…

A:

Q: (-1)"(2n–1) Σ n(n– 1) n=2 IM:

A:

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: (a) {cos ((2n + 1)E)-1 n=1 (Ъ) e2n+1 n=1 (c) n³ + n² – n2 + 3 - 1 | n=1 (d) {nsin 프}. n n=1

A: due to time limit I am able to solve first 4 part

Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

A:

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: 4n + 7 Σ (i) (ї) Z(n² – 8n + 16) 5n n=1 n=5 8

A:

Q: Question 9 Is 2n² + 12n + 18 equivalent to (2n + 6) (n + 3)? True O False Question 10 Is 12n + 18…

A: Note - ( As you asked multiple questions , According to our guidelines we will answer first three…

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: Problem 5.3 Prove that n n(n + 1)(2n + 1) (3n² + 3n – 1) - Σ- 30 j=1

A: We have to prove given result by Principle of Mathematical Induction.

Q: (– 1)n+1x2n+2 n=1 3n+1(2n+ 1)! (– 1)"-1x²n-1 Σ n=1 30-1(2n - 2)! Some other answer (– 1)"+1x2n+3 Σ…

A: We have to choose the correct answer from the given option

Q: 4 - 2 4 Compute A - 513 and (5I3 )A, where A = -4 2 -6 - 2 2 2

A:

Q: Find L {(2 t" – 3) (t" + 2)} O 2(2n)! n! 82n+1 sn+1 2(2n)! n! - 82n+1 sn+1 O 4 n! 82n+1 n! n+1 O…

A:

Q: 13 + 33 + 53 + + (2n – 1)3 = n²(2n² – 1) - ... Ensure that you explain the steps taken.

A:

Q: ¸1(1 + r)n−¹ − 1. (n-1-1₁ r Sn (1+r)"So - P[- =

A: Sn = 1+rnS0 - P1+rn-1-1rAim: To find expression for 'n'.…

Q: 7|32n+1 + 2n+2, Vn E Z.

A:

Q: 8. Ση-0 ne-1 4n 9. En=0 (n+2)3 n=0 (n+2)³ 3. 10. Σ0 n-3n+2 %30 n2-3n+2

A:

Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

A:

Q: Find the sum of the following: 1 Σ 5n² +5n n=1 a. b. n=1 3+2-1 4n

A: a) ∑n=1∞15n2+5nb) ∑n=1∞3+2n-14n series converges: The series  ∑n=1∞an converges to k, then the…

Q: 2+4+... +n lim 7n2 + yn

A: limn→∞2+4+....+n7n2+n

Q: (-1)".n -1)".n 5n+2

A:

Q: 1 Vn > 0, 2(аn+1 — аn) %- 2n

A: Given an=1-12n so an+1=1-12n+1.

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: (2п)! Zn=1 2n.n!

A:

Q: n° n=1 3n2 en Σ: 22n 2 2n + 1 n=1

A: Since you have posted multiple question in this question which are not interlinked so i have solved…