1 Σ (-3)²+" (n² + 1) -(4x – 12)" n n=0

Q: 20. What is the value of the 4th term of the expansion of (y + 2z)°? 16y"z 448y 23 25628

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Q: La función f(x) =* expresada como serie de potencias es 4-х xn+1 А. 22n+1 n=0 4xn+1 В. 22n+1 n=0 C.…

A: Given function is fx=2x4−x. We have to find the power series representation of the given function…

Q: n(n+1)(2n+1) 2.Prove k2 = for n > 1. 6. k=1

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Q: 5. Give a general form for T(n) for n > 2

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Q: %3D k (n+1) (k-10 (n+1) k +1 (*) n+1)

A: The correct option is the last option. The detailed solution is as follows below:

Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: arctan(n) (iv) (-1)". n3 +n +1 n=1 [ Select ] n! 5n n=1

A: Solve the 4 and 5

Q: B. Suppose that y1, Y2, ., YnidN (0, o2). We wish to find the most powerful test for Ho:02 = o3…

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Q: [3n+ 2 (-1)A In 3n + 6 n=1

A: Express the alternative series test for convergence. If ∑n=1∞(-1)nan or ∑n=1∞(-1)n+1an converges if…

Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

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: 8. 3n+1 .251-n n#1

A: We have to solve given problem:

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.

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Q: k-1, O A. (n+1)! (k-1)!(n-k)! (n+1) В. (k-1)(n-k+2) OB. С. (n+1)! (k-1):(n-k+2)! D. (n+1)!…

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Q: 3- 2 GL 1- 7654 321 42345 67 -1- -3 723

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Q: (a) > [Integral Test] n2 + 108 n=1 1 ( b) Σ (2n + 3)17 [Comparison Test] n=1

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Q: 2) S(n)-10-2 at n 5

A: Given ,  f(n) = 10 (2)n     ......... (1) We have to find the value at n = 5 Put ,  n = 5 in…

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

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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: -xx-9 and y=-x+3 у -9-8-7-6-5-4-3 1 y=x: POINT(S): IN 76 NWA -2 N3456789 -2 -3 -6 -7 -8 23456 -9 +2…

A: We have to find the graph

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

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

A: Answer

Q: Show that n*-n3.5+300n + 234n²log n³ + nVn10 e 0(n*)

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Q: Show that for any 1 ≤k≤n. T (1) = n²(n²-1²)...(n² (k − 1)²) 1.3.5 (2k-1)

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Q: Find L {(2t" – 3)° } . | O 4(2n)! 2n+1 12(n!) + sn+1 4(2n)! g2n+1 [ 2(n!) 8n+1 O 4(n²)! 12n! 9.…

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Q: 9n – 5 a) lim n-- 3-n - 18 1 2n2 + 3n – 5 8n? +1 1 b) lim n- o0 || 4

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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

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

Q: 1. Find the coefficient of x5y3 in expansion of the expression (x + 3y)8 2. Sixteen people attend a…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: Ex : Express the Sum o+ 2 +4+6+8 in Sigma nata tion. K = -2 %3D -2

A: First we find nth term of AP then replace k by k+3

Q: is equal to. k=1 n2 The sum O n+1 2n O n+1 O n? +1 2n2

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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: 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: 2. Given ON=4x NE = 3x +8 OE = 36 36 %3D 0 4x N 3x+8 E ON + NE = OE

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Q: Proceed as in Example 3 in Section 6.1 to rewrite the given expression using a single power n(n –…

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Q: cos(n") In(4) 1. 1 2. n In(n) n%3D 6n + 3 (-1)" n=1 1 4. n - 5 3.

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Q: 14) Calculate the 5th term in the expansion of (x – 2y)7.

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Q: (5) Show that T(n)o(n) > n for all n E N. 11

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Q: 2s+2 ds = In\s| – In|s + 2| + C s+3s2+2s

A: Given :       ∫2s+2s3+3s2+2sds=ln s-lns+2+C

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: [from n=4 to infinity] E (2/3)3n-1 (-4/7)2n+3 *that E just means that sum symbol.

A: Let\'s say the sum of the series is S. Hence S will be as shown on the white board. Please note the…

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

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

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

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Q: 3n – 5n is n→ o n° - 2n² +1 lim 3

A: It is given that, limn→∞3n3-5nn3-2n2+1.We have to evaluate it.

Q: -6an-1 for n > 2 with the initial condition a = -9. an an

A: Given an = -6an-1

Q: 7. E(-1)"- Vn +1 n=1

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Q: 2n2 – 4n +1 is even → n is odd

A: