1 Prove 2.5 1 1 + .…+ 8.11 1 for n > 1. %3D 5.8 (3n-1)(3n+2)

Q: 2 If C = |2 -1 0 Show that (C")-1 = (C-')" -2 2 2

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Q: Find L[14cos28t] 7s s2–256 7. 2s 7s + s2+256 s2+8 7s s2+64 1

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Q: 1. Prove the following equality by induction: 1- 22 + 32 – 4? +. + (2n - 1)? - (2n)² = -n(2n + 1),…

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Q: (b) 2+4+6++ (2k) = k² + k and 1+3+5+ ... + (2k − 1) = k² (k = 1,2...).

A: Alternative Interpretations and Solutions: 1. Verification by Substitution for Specific Values of…

Q: of 2 + [y] 8+ {2 ²³ = 12; n 3+2=13°54 and {n} + y + 2-472 y + [2] = 14.7 then find

A: Given: x + [y] + {z} = 12 [x] + {y} + z = 13.54 {x} + y + [z] = 14.7 We need to calculate the value…

Q: e2x -dx =D 1+ex (A e2x + In(1+ e*) + c B 2e2x – In(1+ e*) + C © e2x – In(1 + e*) + C D ex- In(1+ e*)…

A: Integration

Q: Which of the following statement is always true? (a) p(2n) = p(n) (b) p(n) is always even. (c) Edin…

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Q: n Find I (1) n=2

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Q: ..+n = n(n +1) 2. prove that 1+2 +3+ %3D for n=L,2, 3

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Q: 3 Which of the following expressions are equivalent to 6n2 +12n 18 (n+2) C 6n (n+2) 18n + 38 A 6n…

A: The addition(subtraction) between two like fractions can be done by adding(subtracting) the…

Q: 8. Determine (MN)-1 where M (:) 5 and N -5 2

A: The given matrices are M=8541  and  N=5-1-52. Evaluate MN as follows.…

Q: Problem 8.1. Show: for all neZ+, we have (1 + 1) + (1 + 3) + (1 + 5) +...+(1+ (2n-1)) = n² + n.

A: The above given mathemtical statement depends on set of natural numbers. Therefore, we can use…

Q: 1 2 3 4 , Q10- If 8 9 7 6 5 1-find Det.? 2- (1/Det.)(A) 4 5

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Q: 5. Given: 4(5n + 7) – 3n = 3(4n – 9) Prove: n = -11 %3D Statements

A: Topic = Algebra

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

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Q: Remind yourself what () means. For this class, we will use the convention that () = 0 if n < k or if…

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Q: Determine whether (5) () = (;) (") n-3 (where 3 < k < n) is true or %3D false. O True O False

A: We have given that

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

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Q: 4n2 +14n +1 c. Let P(n):9+13+...+(4n+5) = Show P(k) P(k+1). Is P(n) true Vintegersn21? 10 Fon the…

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Q: Σ s2 an convergent or divergent?

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Q: Which of the following is the value of the coefficient y on the right side of the equation given…

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Q: 5. Find and prove a formula for P(n,n-2) for n2 3.

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Q: (d) Prove that 2" +3" is a multiple of 5 for all odd n E N.

A: Use the mathematical induction to prove the given statement.

Q: Show that c12 2 dx = ln (7 + 4v/3). 8, Va2 – 8x -

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Q: Find L(3t + 13]. + 13 s2 13 (8-1)2 13 2 + 13

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Q: (7) Let X = P(2) and E-x)= E(5– 5x), then 2 is. (a) 25/26 (b) 26/25 (c) 12/26 (d) 26 (e) None of…

A: Given X~Pλ and E15x=E5-5x

Q: 1 2. Find L-1 [ s2-8s+25

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Q: 198 k=0 (4k)! (²k+¹) 2k 28k (2k)! (2k + 1)! 1 13 + 1 15

A: note : Since you have posted multiple questions, we will provide the solution only to the first…

Q: (i) in n(n+ 1) r = r=1 (ii) n(n+ 1) (2n + 1) 6. r=1 (iii) in 2. n(n+1)]2 3

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Q: Are there any other ways of decomposing 1/11 into sum of two unit fractions? In how many ways can we…

A: Decomposing Unit FractionsThe problem of decomposing a unit fraction as the sum of two other unit…

Q: 2 (i) Show that the result 1+ 5+9 +... + (4n – 3) = n(2n – 1) is true %3D for the casen= 1. (ii)…

A: The given question mainly depends on the the sum of the sequence which is in the form of arithmetic…

Q: 2n (1 -x) (2n+1)! (2) こ

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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

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.