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

Q: (2) |R| = |2N].

A:

Q: 4-The equation x^2+2x-3=O has only one root in the open interval O a. (-2,0). O b. (-1,1). O c.…

A: Thus is a quadratic equation we can find the roots of the equation by solving them

Q: 2. Find an explicit formula for аn 3 За,-1+ 10ар-2 and ao %3D 0, ај 3D 7 An where

A: The solution is given as

Q: (n² – 3n – 21) ÷ (n –7) -

A:

Q: 3 ve AB: BBT = ? A FIND 7. 4 2 OA) 2 -1 4 -2] OB) -2 1 [] --4 2° 2 1 OD) -4 2 OE) 2 -1

A: We have to find BBT .

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

A:

Q: 8. Provide justification for you what will appear on the ex asked. (-1)" (2n)! (a) n=1 n4 – 4n -

A:

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

A:

Q: )- ニ ZS+ト 32 |ニ2+

A: To solve the equation: x+y+z=12x-4y-3z=9-3x+2y+5z=-5

Q: verify the given equation. 16.∞∑n=0an(x−1)n+1=∞∑n=1an−1(x−1)n

A:

Q: Solve the initial value problem dt = 4t + 612, y (1) = 3. (Use symbolic notation and fractions where…

A: Given:  To solve the initial value problem dydt=4t+6t2, y1=3

Q: 2 2/The third term of a geometric sequace whose First term 2 and its FiFth tom 162 is ? A- az a 18…

A:

Q: 2) By using the iterative formula x+1= and x, 1.5, then the value of x, is O 0.3652 O 1.3652 10 of…

A: Given That :  x2+4x=10 and  xn+1=10xn+1 is the iterative formula for the given equation in [1,2] and…

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

A:

Q: 5. = P - p2 Ans: = cet dt 1-P

A:

Q: 5) Show that n(n+1)(4n-1) E"=1 r(2r – 1) 6 Hence find E015 r(2r – 1) |

A:

Q: to: explicitly state the te- Σ2/ n=1

A:

Q: (-1)"(n + 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A:

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

A:

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

A:

Q: (-1)" -Σ S. n=1 Vn+1

A:

Q: By using the iterative formula Xn+1 and xo = O O 0.3652 O 1.3652 O2.6352 = 1.5, then the value of x5…

A: Find the value

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: a) Suppose, T(n) = 1²+2²+3²+..+n2. Show that, T(n) is in O(n³). %3D .....

A: Big-⊖Notation: Let f and g be real valued functions and assume g is eventually position. We say that…

Q: (-1)"(n+ 2) 2n+1(n + 1) 4. Compute the exact value of n=0

A: Given series is  ∑n=0∞-1nn+22n+1n+1

Q: 5.7.4. Show that the two formulas (r = y) and (S(r) = Š(y)) in N.

A: Hi, since there are 2 questions given, the first one is answered.  Given - The formula  x=y To prove…

Q: Let A={mez: m = 2a for some aeZ}, B= {mez: m = 2a for some aeZ}. Show that A=B. (need to show A≤B…

A:

Q: 38) - con A) 0 sec B) 5π T, 13л 5т D) 0 3 12 12

A: Find the value of x which satisfy sec(x/2)=cos(x/2)

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: 8. How many integer solutions are there to the inequality Y1 + y2 + Y3+ y4 0, 0 < y2 ≤ 10, 0≤ Y3 ≤…

A:

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

A: We use partial fraction method to find the required sum of the series.

Q: 7. What necessary and sufficient condition do you need to impose on an integer c so that the…

A:

Q: 14. Find all solutions to 2sin(5x)-3V3 =-4/3. State exact values only. %3D

A: Given equation, 2sin5x-33=-43

Q: 2. Show that coo(N) co(N) § c(N) Ę e^(N).

A: To prove that c00N⊂c0N⊂cN⊂l∞N. By definition, c00=x∈lp|all but finitely many xj's are zeroc=x∈l∞|xj…

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

A:

Q: Solve for n if nEN: (4+8+12+ ... +4(n-1)) + (2+4.5+7+. .. 4+5n -%3D126.5 2

A: Sum of n natural numbers is n(n+1)/2.

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

A:

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

A:

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

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: (*") = (") + G) + 5. Prove + 2n2. %3D

A:

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

A: limn→∞2+4+....+n7n2+n

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: