10. Use the formula (3k-1)(k-4) = n-5n²-2n, V ne Z* to calculate k-1 20 the sum (-6)+ (-10) + (-8) + 0 + ... + 840 + 944 = E(3k-1)(k-4). k-1

Q: n 2n + 2 /2 n 2n k k=1 \k –1, п+1 n -

A: The objective is to prove that ∑k=1nnknk-1=2n+2n+1/2-2nn This theorem can be proved by induction,…

Q: Also, from Theorem 4.9', we have k2k-1 k2k [(E – 2)(E – 1)(E +2)]¬!2* (4.239a) (1 · 4)(1!)…

A: The one is red is [(E-2)(E-1)(E+2)]-12k=k2k-1(1*4)(1!)=k2k8        (1)y(P)k=-79k-k26+k2k8…

Q: Find the interval of convergence for the figure below

A: 1. ∑n=0∞ (-5)nn!(x+10)n2. ∑n=0∞ n!(x+5)n3. ∑n=0∞ en(x-2)n4. ∑n=0∞ (x+4)n(n ln n)2

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

A:

Q: A white wine at room temperature 70ºF is chilled in ice (32ºF). If it takes 15 min for the wine to…

A: Let's find.

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: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

A:

Q: Find the radius of convergence and interval of convergence of  Σ 2 to infinity ((x+2)^n)/(2^n)(ln n)

A:

Q: 4 The value of 2 n=1 3n2 will be + 6n .... .

A: See solution below

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

A: given sequence  -1n+1x2n-12n-1!

Q: The solution of e² = - 11 has the form x + ily + 2nn) where n is an integer. What is the value of x?…

A: The given equation is                                                ez=-11

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

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

A: Explanation is given as follows:

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

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

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

A: Answer

Q: (-1)"n²(x+3)" 2. 5n n=1

A: Radius of convergence

Q: 4. 43 + n+3 n'+6n+9 5. 부-부 x*+38 x-5 13x-2 6. x-5 7. *- у 3y 3 8. c+2 c-3

A: Consider the first expression:…

Q: Find (2n – 3)(n + 4). * О Зn +1 О 2n^2 + 5n -12 О 2n^2- 12 О 2n^2 + 11п +1 Simplify: 2a^2(5а- 6) -…

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

A:

Q: - What is 10% of a number whose sum of 15% and 6/10 of which is 450?

A:

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: 5) h(n) =-2n² + 4; Find h(4)

A:

Q: 2n zn こ (n) n:0

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

Q: If a_1=9a1​=9 and a_n=4a_{n-1}an​=4an−1​ then find the value of a_5a5

A:

Q: 10) Which of the following shows the solution for n2 + 2n 2 24? A) 4十 -6-5-4-3-2-10 123456

A: The given inequality is n2+2n≥24

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: 21. Solve the problems belows. -16 + 5n = -7(-6 +8n) +3 -10n + 3(8 + 8n)= -6(n - 4) 10(x +…

A:

Q: Example 9.10. Solve yn2-4y = n² + n - 1.

A: The solution is given as

Q: 2" (a) 3 3n+1 (c) E(-1)"; 4n n=1 (b) 3+5n² (4) E n+ n2 n=1 n=1

A:

Q: motorist is pumping gas into his car at a rate of 5/12 of a gallon every 1/24 of a minute. At this…

A: Here we want to Know how many gas will pump into his car in 1/2 minutes.

Q: 3.6...(3n) E=1(-1)" n=1 2n2.5...(3n-1)

A:

Q: The sum of 8n- 3n +10 and-3n²-6n-7 is 1) 5n-9n +3 2) 5n-3n-17 3) -11n-9n-17 4) -11n-3n +3

A: Given Data: Expression 1: 8n2-3n+10 Expression 2: -3n2-6n-7

Q: 13. What is the sum of 5-14 2410z+21 3x2+14x-10 (2+7)(z-2)(z+3) O 32-14r-10 (z+3)(z+5)(z+2) » " #-3,…

A:

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&lt;1 Check the convergence of the…

Q: -3 -5 2 -3 -5 2 d. Suppose that E4 -2 -3 -3 -4 -6 -6 4 -4 4 -4 Find E4 and E,'. E4 = 3. II 3.

A: Given: E4-3-52-2-3-343-4=-3-52-4-6-643-4

Q: B. Use combinatorial proof to solve the following problems 1. (;) (:3) = (2) (3) п-2 \k-2,

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: 11) Which of the following shows the solution for n2- 2n < 24? 十十 A) 6-54-3-2-10123456 + +++++++…

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: The sum of 8n^2-3n+10 and -3n^2-6n-7

A: Sum of 8n2-3n+10 and -3n2-6n-7       = 8n2-3n+10 + (-3n2-6n-7)        We will add given expression…

Q: 13) b - 6b + 8 14) n + 6n + 8 15) 2n + 6n - 108 16) Sn' + 10n + 20

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…