2n2 – 4n +1 is even → n is odd

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

A:

Q: Q5: prove 1) e2-j3n-e² = 2) |e²| = ex

A:

Q: (-1)" n+1 nEN. E = %3D n

A:

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

A:

Q: n2 – n 1 2n² + n الم نابعة زختبر تقارب -

A:

Q: 2. {x|x = -29° + n360°} = {x|x = 331° + n360°} where n is any interger.

A: (2) Given- x|x=-29°+n360°=x|x=331°+n360° To find- The above statement is correct or not.

Q: { :Find the first 3 terms for 2n-1 (2n-1)! (−1)n+¹

A: given sequence  -1n+1x2n-12n-1!

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

A:

Q: Oa, 1+ 16a, 2+ 225n for n> 2 with initial conditions ag = -23, a1 -19.

A: Given recurrance relation is  an=16an-2+225n     , n≥2 and initial conditions are a0=-23, a1=-19

Q: n 5n (2)2n=1 2n

A:

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

A:

Q: -2n2n 2n n 2) п En=1 1 —

A: Given series is ∑n=1∞1-2n2nn2n

Q: 2 2n² 1-n²¹ 1+n³ 1+n³ 202-1-n 3 1+n³ Simplify Show your work. 2

A: Simplifying the given expression

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

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

Q: Use the substitution method to show that the solution of T(n) = 2T(n/3) + n2is O(n2)

A: Given that T(n)=2Tn3+n2 To show that it is O(n2).

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

A:

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

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

A:

Q: -4 -2 Let E= 0 Find 2E. -3 5

A: Given,  E=-4-204-35

Q: If x1=2, Xn=4X(n=1)–4n Vn22. Find the general term xn

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: 4 Σ n2 +4n +3 - 9-n+24n+1

A: Separate the sum.

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<1. Simplify the numerator of the given…

Q: 1. Solve: An = An -1+ n; Ao = 0

A: As per our guidelines we are supposed to solve only one question. For the solution of the first…

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

A:

Q: 5) h(n) =-2n² + 4; Find h(4)

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Q: (-1)"(2n–1) Σ n(n– 1) n=2 IM:

A:

Q: 4n +1 (a) 2n2 +3 n=0 5n2 – n+1

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

Q: μ1 = μ2 = 0, n2 = 27 and n1 = 19; thus df is:

A: Given that, μ1 = 0, μ2 = 0, n1 = 19, n2 = 27. df is degrees of freedom for testing the hypothesis,…

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

A: The ratio test can be used to assess if a series is converging or diverging. The following are the…

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

A:

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: In what case of k such that there is only one solution? 2x + ky = 10 kx + 2y = -10

A:

Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively ,Prove that S3=3(S2-S1)

A:

Q: 9. Solve the following equation. sec x - 2 -0 A) 元 x -+ 2n and x- 2n7, where n is an integer 6 B) x…

A: Given: sec x-2=0

Q: 너 ()- 3s %3D O 3te-24 O 3e-24 (1 + 2t) O 3e-24 (1 – 21) O 3e (1 + 21) O n (금) O 6te2 O 31e2

A:

Q: If X~N(0,1) then X2~

A: In question,  Given that X~N(0,1). Then we'll find the distribution of X2. he solution is below,

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

A: limn→∞2+4+....+n7n2+n

Q: 4 and for n > 3, an 2an-1 + an-2 + 5n, express an in terms of n %3D 2. Let, a1 = 3, a2

A:

Q: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

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: 6. Between z= -1.53 and z=0

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Q: (2п)! Zn=1 2n.n!

A:

Q: what are the first six terms of f(n)= (2n)/(n+2) ?

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Q: 2 -3 +21 -1 0 2 Find A in AT+ -1-3

A: Given:AT+52-1-3-1=2-3-10+2I Let the matrix A be,A=abcdAT=acbd So,…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.