1+ x Σ Aa" (1 – 2)? n=0

Q: n Rị |1-Ri Lecen (A) = II [A exp(-AZ,)]“ [exp(-ar)] z.)][exp(-Ar)]" i=1

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Q: (n² – 3n – 21) ÷ (n –7) -

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Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively.Prove that S3=3(S2-S1)

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Q: n Find the general solution of o ( :) (2)*y(n-i) =0. ata of any nonzero real

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Q: 3) FIND A PARTICULAR SOLUTION OF THE ODE y"+8y-20y = 2x +5 - e?X %3D

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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: (a) an = }(n² + n). (b) an = 2an-1 – an-2 with ao = 0 and aj = 1. (c) an = nan-1 with ao = 1. %3D

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

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Q: 2) FIND THE INTERVAL OF CONV. * (x-1)^" 2 (n+i) n=0

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Q: (b) Define fo = 0, f₁ = 1 and fn = fn-1 + fn-2 for n ≥2. Show that 3 fak for all k ≥ 0.

A: As per the guidelines we shall solve one question only as you have asked more than one different…

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: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

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

A: Answer

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: f in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n then prove that…

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

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: The following table shows the result of inoculation against cholera: Not Attacked Attacked 5 (AB) 9…

A: Hypotheses: H1:The effect of inoculation and Cholera are independent Ha:The effect of inoculation…

Q: use gauss's trick to determine R(n)=2+3+4+...+(n-1)+n+(n+1)

A: It is known that sum of first n numbers is n(n+1)2  that is  1+2+3+----+n=n(n+1)2 Gauss trick method…

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&lt;1. Simplify the numerator of the given…

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: 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) 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: 2 1.5 0.6 09 1.2 Reason for similarity?i * SSS- * SAS- H AA 1 NNS

A: SSS (Side-Side-Side) SSS Similarity Theorem: If all three pairs of corresponding sides of two…

Q: () 2k = 3", Vn E N k k=0 k n+1 Σ 2 Vn E N, n > 1 3 k=2 į * () 主) n 3k = 4", Vn E N %3D k k=0 = 2"-1,…

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

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

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Q: Describe the long run behavior of f(n) = 3n – 4n³ – 5n° + 5 As n → - 0, f(n) → ? As n → o, f(n) → ?

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Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively ,Prove that S3=3(S2-S1)

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

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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…

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Q: n(n – 1) is O(n²). 2 Show that

A: f(n) is O(g(n)) if there exist positive constants c and k such that f(n)≤c g(n) whenever n&gt;k.…

Q: z/(z-3)2 dz ; C: |z+3| =3 slove by residue theorem

A: The given integral is,

Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

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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: Show that for any n E N, n(n + 1)(2n + 1) %3D k=0

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Q: Find a formula for Sn, n > 1, if sn is given by 6 7 3' 5' 7' 9' 11 4 8 - Sn =

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Q: 2) al X, X2 ,-.,Xn ~lid exporentíal ( 4 100/ b) Xg, Xz,=-- Xn~íid N(44i 44)=) 9= E Xi ~ ? %3=…

A: It is an important part of statistics. It is widely used.

Q: (In 2x)' In V k.

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

A: limn→∞2+4+....+n7n2+n

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: (-1) is where n is an integer. equal to the above e(1+2n)i where n is an integer. equal to the abov…

A: We know from eular formula e^iθ = cos θ + isin θ

Q: If the statement is true, prove. If the statement is false, disprove. 1 + 2" > 3n for all n E Z

A: False.  take n =2

Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: (b) Show that V n 20 > (2i +3)3' = (n+ 1)3"+1. i=0

A: To Show- Show that ∀ n ≥ 0 ∑i=0n2i + 33i = n + 13n+1.

Q: (3b) Let n E Z. Prove that if 3|(2n² + 1), then 3 ł n

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Q: Consider the systenm o o-21 x + %3D 0 3 Frnel the ennit s tep esponse of the system.

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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…