N :3 lim N4 j=l N >j = 1+2+ +N = N(N + 1) N2 N j=1 2 2 N P=D 12 +22 + ...+ N² N(N + 1)(2N +1) N3 N? N j=1 3 2 N E = 13 +23 +...+ N³ = N?(N + 1)2 N4 N3 N2 j=1 4 4 4 +

Q: Let n E N*. a. Let a > 0. Then 1 as n 0o. b. - 0 as n → ∞ n16/5+2 c. (-1)"+1"" → 0 as n → 0 d.…

A: We know that limx→∞1x=0. It implies that if x→∞, then 1x→0. We need to calculate the limit for every…

Q: Use linearity and formulas attached to rewrite and evaluate the sums.

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Q: The sum of the series 1) is 1 n =1n+1 O A. -1 О в. 1 OC.O O D.1 O E. a 10 1/2 立

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Q: 2) h(n) = n² - 5 g(n) = -4n + 5 Find (ho g)(n) %3D

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Q: (-2)"+1 n+ 5" (2n)! 2n - n! - n (a) (b) (-1)". n=1 n=1 (c) E(-1)": (n!)'3" (2n + 1)! (d) 5 (-1)"…

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Q: The series 2 ÷, n =0 x" |x| >1 has a sum equal to: Select one: а. х b. х— 1 C. 1 1-x d. 1 х —1

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Q: (-1)"-1 5+ Vn 1. n=1 3 2. 1+νη n=1 5+ νη 1+ νη 3. n=D1 1 2η 4. 3+ νη n=D1 1 5. I (-1)°, (-1)*.

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

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Q: TL ( - k) = | k-1 a. 6n + (n + 1)(2n + 1) - b. n(n + 1)(2n + 1) c(n²-1) C. O d. n3 e. 00 f. 플 (n +…

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Q: The solution of e² = -2 for n = 0,±1,±2,. is %3D ... Select one: O a. In2 + in(1+n) O b. In2 +…

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Q: n-1 n-1 k n-2 n-2 - = P k X6n-10 X6n-9 = 4 - n-1 п-1 n-1 h k k n-1 X'6n-8 = r X'6n-7 = P h - . k - 4…

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Q: 4. The series r ? is divergent for rul A >1 B k>2 c k< 2 D 0<k<2 A

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Q: 2n 9.What are the first three terms of the series n=1 O A. 2 4 x2 O B. 2 4 6 x2 'x4'x6 О с. 2 4 6.…

A: Given, The series  ∑n=1∞2nxn We have to find first three terms of the series .

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: (x-1)" Which are the values of for which the series n=1 n A. 0SX<2 O B. -1<x<1 O C.0<x<2 O D. -1sxs1

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Q: n If f(x) = -x" and n2 + 1 n=0 n g(æ) E(- 1)". -x" , find the power series of %3D | n- + 1 n=0 1…

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Q: Which of the following is TRUE? 2x2+1is n(x2) since Cx222x²+1 for all x 21 where C=3. OA. n is a (n3…

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Q: 0.8 0.9 1.0 1.1 1.2 1.3 j(x) 0.368842 0.405950 0.440051 | 0.477092 0.498289 0.522023 p(p -1)(p fp =…

A: Using the bessel's formula, The value of function at x =1.055 Taking the origin at x0=1.0 , h=0.1 We…

Q: The power series representation of the function r 2 1 xn+5 is given by x +2 (a) 2n+1 n=0 (b) ) (-1)"…

A: We will rearrange the given function into known formulas to find the respective power series.

Q: Σ 2n If C(x) = 00 -22n and S(x) = 2n +1 -22n +1, find the power series of C(æ) + S(x). n=0 32n 32n+1…

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Q: 2n x2n and S(x) 32n 2n + 1 If C(x) : r2n +1 32n +1 find the power series of C(x) + S(x). n=0 n=0 n=0

A: Given: C(x)=∑n=0∞2n32nx2n and S(x)=∑n=0∞2n+132n+1x2n+1To Find: C(x)+S(x)

Q: E-o(-1)"(n+ 1) x“ = (1+x)² 1 2.b) for |x| < 1 %3D n=0

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Q: Ex : Express the Sum o+ 2+4+6+8 in Sigma nata tion. -2

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

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Q: f(n) = n³, g(n) = 6n + 1 е.

A: Given: e) f(n)=n3 and g(n)=6n+1 To find: a and n0 such that a·f(n)≥g(n)

Q: 98 unfornly distributed the death cre CHX+h) then nen 2n+n M Prove t 2+h pmx

A: If the deaths re uniformly distributed in the interval (x,x+n) Then  qnn=2n*Mxn2+n*Mxn suppose qnn…

Q: 1/n ( e) E- (In n) VIn² n– 1 n-3 (f) E(-191 \n+1 n=1 n+1 ( g) š(-100)" n! n=1 1 (h) E: 'n(1+In² n)…

A: The nth partial sum of a seriesS=∑1∞an is defined as Sn=∑1nan. The series is convergent, if the…

Q: (k² – k) = O a. n? O b. n(n + 1)(2n + 1) O c. 6n + (n +1)(2n + 1) O d. (n + 1) O e. 플 (12-1) O f. 00…

A: the given expression is: ∑k=1n k3-k we have to find the value of the given expression.

Q: 4 Σ E Vn +1 n=-1

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Q: 3. Determine which of the fol 2" (a) n=1 n! (d 1 (b) (e n=1 2n 3n n+1 (c) (E 3n n=1

A: Since you have posted multiple questions i can do first three subparts as per our company guidelines…

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…

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Q: (2 2" (2"-1)a - 3 If A = then A" = Éro* +1) = -m(n + 1)(a° +n+2) 4 5 Ertr-1)=,n(n² - 1(3n + 2) 12…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 5n2 For E>0, there is a corresponding N such that -4/0 N. 4 +3 Then the value of L will be

A: Given function is , f(n)=5n24n+3

Q: A production manager determines that t months after production on a new product begins,  the number…

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Q: Find L {(2 t" – 3) (t" + 2)} O 2(2n)! n! 82n+1 sn+1 2(2n)! n! - 82n+1 sn+1 O 4 n! 82n+1 n! n+1 O…

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Q: The series 1 + vn- 1 + Vna n=1 8

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Q: L %3D e2t e-3s-6 (s+2)? O e6-3s ( 1 3 + S+2 (s+2)2 O e-3s (s+2)2 1 3 s+2 O e2-3* ( +) 1 (s+2)2 s+2 O…

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Q: ¸1(1 + r)n−¹ − 1. (n-1-1₁ r Sn (1+r)"So - P[- =

A: Sn = 1+rnS0 - P1+rn-1-1rAim: To find expression for 'n'.…

Q: [1 1 1 If A = 1 1 3"-1 3"-1 3"-1 prove that A" =| 3"-1 %3D 1 1 3"-1 for 1 3"-1 all values of n e N.…

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Q: (k) E(-1)"-1. n+1 n=1 Vn +1- Vn – I (1) n=1

A: The given problem is to determine whether the series is converges or diverges using the appropriate…

Q: (d) (e) n=1 n=1 3n²+ 1 2n² +3 2¹ (n!)² n2(2n!)

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Q: Find L {(2 t" – 3) (t + 2)} 2(2n)! s2n+1 sn+1 O 2 (2n)! $2n+1 n! sn+1 4 n! 82n+1 n! n+1 8. O 2(n²!)…

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Q: (b) Z/n = (q) if and only if kq 0 for all 1 < k <n.

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Q: φ(n) Σ× + Σφ) i=1 d|n Where gcd (X , n) = 1, 1 < X Sn 1 + φ(n) \ n 2 It is not defined in general n…

A: We have to determine the value of given expression : ∑i=1ϕ(n)Xi + ∑d/nϕ(d) , where gcd(Xi , n) = 1,…

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

A: Find the radius of convergence and interval of convergence of given infinite series.

Q: x2 x+2 Q2) k(x) V2 – x m(x) n(x) 3-х x² + 1 Find a formula for (k o m o n) .

A: Given that k(x)=2-x, mx=x+23-x, and nx=x2x2+1. Find the formula for k∘m∘n. k∘m∘nx=k∘mnx…

Q: Q.20) If ef(x) = 3x² +4, then f'(x) = a) 3x² b) e-f 3x²+4 3n 71 tements applies to the series En-1…

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Q: 15. Determine whether or not the power series (A) is a solution of: y"+6 y'+13 y=0 (neglect terms…

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Q: (k-k) = O a. n O b. 6n +(n + 1)(2n +1) OC. 00 O d. (n + 1) O e. 4(n + 2) (n² - 1)

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Q: (c) Find the sum of each of the following series. (1) E n(n – 1)x", |x| < 1 n = 2 x2 (1–x)3 | n2 - n…

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