2n zn こ (n) n:0

Q: zn 3n+1 7. 4-2n nニ」

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Q: What is the coefficient of the x^7y^4 in the expansion of (x+y)^11

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

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

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Q: 26 E(- 1)"2n - %3D n=0

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

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Q: {15n : п € Z} %3 {3п :п€ Z}n{5n :n€ Z}

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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

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

A: Answer

Q: 2.3 = 0.733 Spuarming on both sides 2 %3D 0.433 x(1- 82) 82=0.5372(1-9e) 8+0.53922 = 1.5372 E = 0.8

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Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: (c) –1)" n'/3 n=1 e2n ( a) Σ (2n)! n=1

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

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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=

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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: What is the coefficient of x'y5 in the expansion of (1x + 3y)18? 3,15

A: Use formula of binomial expansion to solve the question.

Q: 4. You are given: 7800-70t- 1? P30 0SIS TO 7800 Find qso-Hs0-

A: The given formula for tp30 represents the probability of an individual aged 30 years to survive the…

Q: n 4n – 1

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Q: 4n +1 (a) 2n2 +3 n=0 5n2 – n+1

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

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

A: In this question, we prove the sum of squares of natural numbers.

Q: 18) -D°.n 5n+ 2 (-1)".n

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Q: 2n+2 – 3" Σ - 2. Determine 6n+1 n=0

A: To find: ∑n=0∞2n+2-3n6n+1

Q: n²-7n +3 | + 10n-4n2 n2 4 + n3 In (n+2) in(1+4n)

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

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Q: 2(-1)n-1_6" n=1 5n+1

A: To find: ∑n=1∞-1n-16n5n+1

Q: e2a – 6e" – 27 = 0 - -

A: e2x - 6ex -27 = 0 here lets assume ex = y y2 -6y -27 = 0 y2 -9y +3y -27 = 0 y(y-9) +3(y-9) = 0 y+3 =…

Q: Q3.) The value of the product P = IIK-2 (1+) is B.)n + 교 %3D2 k2- A.) n (1 +) C.) D.) 2 (1+) E.) 2n…

A: we are allow to solve one question at a time if you  need rest of answere please upload separately

Q: n(n – 1) is O(n²). 2 Show that

A: f(n) is O(g(n)) if there exist positive constants c and k such that f(n)≤c g(n) whenever n>k.…

Q: n Σ k + 2n + n2 | n k=1

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

Q: (a) (7x)" n! n=1 (b) 00 (-1)"(x – 8)" Vn n=1 (c) 5(-3)"(z – 1)" Vn + 2 n=1

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Q: z²+1 at z = ∞

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Q: 6 - 22n-1 5n+1 n=1 =D1

A: Given: ∑n=1∞6×22n-15n+1 A ∑n=1∞fn series is convergent if, fn+1fn<1 Check the convergence of the…

Q: Σ 2n+3 + n2 +3n n-1 3.

A: Given series ∑n=1∞1n2+3n+2n+33n

Q: (i) ae2* + 2xe²* = 8e2« (ii) e2 – 6e" – 16 = 0 (iii) In z+ In(r – 3) = In(5x – 7)

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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: Σ 2n (2n - 1)2(2n + 1)2 n=1

A: The given series is: ∑n=1∞2n2n-122n+12 By the result of Comparison test, if ∑un and ∑vn are two…

Q: ( W + ) )² + (0-3679K - 1:3679 ) ( W + ₁) + 0-3679 +0-26421-0 -)

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Q: a.Find the coefficient of y3z2 in the expansion of (y+z)5+ (y-z)5. b.Find the coefficient of z17 in…

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

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Q: 1 Vn > 0, 2(аn+1 — аn) %- 2n

A: Given an=1-12n so an+1=1-12n+1.

Q: 2 0 1 -1 4 -1 -1 2 0 1 -4 -2 B = | 0 3 1 2 2. A = 1 4 Find: 2: BT.B1+A?

A: The transpose of the matrix M is obtained by interchanging the rows and column of the matrix  It is…

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

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Q: (2п)! Zn=1 2n.n!

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Q: M(-1)"+1cos²n n = 1

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Q: ở z laya-2.-1) given thatw= In(5x + 2y³ – 3z). B.

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