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

Q: sin(7n) A 1. n2 (-7)" C 2. n=1 (-1)" A 3. 4n + 5 (n + 1)(2² – 1)" - 4. 22n Vn 5. (-1)", n+ 5 C n=1

A: 1. the given series is ∑n=1∞sin7nn2 the given series converges absolutely. therefore, the correct…

Q: f(x) * a = 49 (2n – 1)! 2". 72n + 1 + (x – 49)" n = 1 1 ㅇ윽+>m.72n+ 1.n! 1 (x - 49)" n = 0 1 1:3.5.…

A:

Q: Select one: 2s2 - 2s 6 S-3 O None of these 252 2s + 6 3 3s2 - 3s + 6 2 3s2 3s 6 S-2 Which of the…

A: Topic:- function  Note :- as per our guideline if more than one question uploaded than only first…

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

A:

Q: x2+1 =0 Has soluion in R

A: Solution:

Q: (-1)" Σ Given: sin = x²n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: If xn → 0, then for every e > 0 there exists N e N such that n > N implies xn 0 there exists N € N…

A: Hey, since there are multiple sub parts posted, we will answer first three sub parts. If you want…

Q: (5 + 6t)7 16x* +6sec(x) x-3cos(x) In(x2 – 1) 2e3x + ex³

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Q: 2. an = 3 +- + cos(2nz) п 3. an = In(14n – n) – In(3n° + 2n² + 1) - |

A:

Q: n #1. E(-1)" n = 1 Vn° +2 n cos nT #2. n = 1 2" # 3. E(-1)"(/n+1- /n) n = 1

A:

Q: Σ 1 as a rational function. Express the series x2n n=1

A:

Q: Given: sinx = (-1)" (2п+1)! x2п+1for x € R n=0 Compute the exact value of the sum 0-1)"(2n+1) „2n+…

A:

Q: Find y' to 3 |х — 1 O y = In x2 O x² In V3x + 5

A: Here we use logarithmic properties ln(mn) =n(ln(m)) ln(m/n)=ln(m)-ln(n)

Q: E1 (arctan(2n+1) – arctan(2n – 1)) n=1

A: The given series is: ∑n=1∞tan-1(2n+1)-tan-1(2n-1)

Q: 6) calculate In (2e°)= 11 2= 0.7n 3= 1. || ln5=1.6n7=20 %3D n(2e°)=X L ex =In 2

A:

Q: b) S. 1 /2n+1 n=1 In+1 c) S̟ =E: In° +1 n=1

A: 7) a) The given series to test is S∞=∑n=1∞e-nn. We can use the integral test for checking the…

Q: I    P    R    T ----------    2000    2%    ½ yrs. 500    ----------    10%    7 mos. 175    1030…

A: According to guidelines I solve first 3 subparts so kindly request you to repost the remaining…

Q: 2. Solve f e** using Simpson's 1/3 Rule with n = 8.

A: The Simpson's 13rule is given below by,  ∫abfxdx=h3fx0+4∑i=1, i is oddn-1fxi+2∑i=2, i is…

Q: 5. Solve: (1 + + In x + dæ = (1 – In x) dy

A:

Q: :Find the first 3 terms for (1 (-1)*1 (2n – 1)!J n+1

A: We have to find the first three term of the given series.

Q: :find E10 (-1)(n-1) Zn=1 (n+1)2 %3D1

A:

Q: 9. The value of ¹₁ O True False [Tn (x)]² dx = 0, for each Chebyshev polynomial T₁(x), n > 0.

A:

Q: Σ (-1)" Given: sin x = .2n+1 for x E R (2n + 1)! n=0 (-1)"(2n + 1) 4" (2n + 1)! Compute the exact…

A: Sum of the series, using Taylor series expansion

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: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: Calculate the residue of eZ.e-5=0

A:

Q: Find L {(2 t" – 3) (t +2)} O 2(2n)! n! + s2n+1 6 sn+1 2 (n²!) n! n² +1 sn+1 O 4 n! n! + s2n+1 8n+1 O…

A:

Q: (-1)"zən+1 (2n + 1)! sin = 3! (-1)"-2" (2n)! 21 1+r+ (-1)*+1," I+1) -E n-1 2! Pip- 1)(p – 2)a.. 3!

A: f(x)=f(0)+xf'(0)1!+x2f''(0)2!+x3f'''(0)3!+x4f'''(0)4!+ ⋯ +

Q: Find L {(2 t" - 3) (t +2)} O 2(2n)! n! -- $2n+1 sn+1 O 2(2n)! s2n+1 n! sn+1 O 2(n²!) n²+1 n! sn+1 O…

A: To find:- L{(2tn-3) (tn+2) }

Q: 18. Evaluate fe³x cos 8x dx e3x a. [8sin 8x 3 cos 8x] + C 3x b. [8sin 8x + 3 cos 8x] + C 73 C. d.…

A:

Q: n=1 B. E(-1)"- In n n=2 1 Inn c.(-1)"+1. n- Inn (-1)*+1. n + n=1 E.(-1)" sin(n) n=1 E(-1)"- n=2…

A: This is a problem of series calculation. based on the several available tests we can determine which…

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A: Given

Q: 4. Compute the exact value of (-1)"(n+2) xn+1 Ln=0 2n+1 (nt1) 100

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

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

A:

Q: 34) Ź (K²_2K) is e (n3) Ź ķ? ビ=3 Ź 2K = k=3 ntro)(2n+1), entntt) Sungs are さ。 2n3+ 3n?+n – ant- Gn…

A: We have solve the given  problem

Q: 1. In(6n) n4 - 2 3. n(In(n))2 %3D2 4. 1 5. nyn sin (4n) 6. n2 n=1 2.

A: We use different kind of series convergent set.

Q: n2 for all n E N. 4n Let r, :=

A:

Q: 33. If z = [i(cos 0 + isin 0)]" then arg(2) -2n0 + n A n0 + n 2n0 D 2n0 – n

A:

Q: 00 2n+4" (1) E n=1n+6"+1 (2) En ( 3) Σ cos [(2n+1)!]? (1-2n)" 00 00 1 (4) E n" (5) E arctan n n=1

A:

Q: 3. Expand cos'x as a series of ascending powers of x. OS

A: To expand cos^2x as a series of ascending powers of x.

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: centered at z = -1. (-1)" (n + 1)(x + 1)" n+1 E"(z + 1)" Σ n! O m-0 El-1)~ (n + 1), (x+1)" n!

A: 1. The function given is fx=1x2. At x=-1, f-1=1. Finding the derivative of the function at x=-1. The…

Q: • 8 If In = 7/2 e*cos" x dx, where n 2 2, prove that: %3D (a) In = 1-n[" /2 e-* sin x. cos"-1 x dx…

A:

Q: -) {in(6n) 2 n=2 =) an = In(6n³ – 4) – ) {cos(nt)}0 n=0

A: e) an=ln6n3-4-ln3n3+5n2-7n+8 determine if the series is convergent or divergent? if convergent find…

Q: Evaluate the given sums for number 5

A: Given,

Q: 5n+7 Find supremum of A :|n E N 4n+12

A: Given set isℝ A = 5n+74n+12 | n∈ℕ We know that a number u is the supremum of a nonempty subset S of…

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

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Q: n +1 5n An bn n + 2' 4n2 – 3' { 400/n -1/(400n2) n even { Į 7 n/(1+n²) 1 901 п оdd Cn dn

A:

Q: (-1)"x²n = E-0 x" and cos x = 0 100 For #6, given that find a power series 1-x (2n)! representation…

A:

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.