2 2 n(n-1)x", n²-n 37

Q: Show that P(n, 1) + P(n, 2) = (22) – 2 (2), for integers n ≥ 2.

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Q: 3 21. (k +1) k=1

A: The given expression is, ∑k=13(k2+1) To find the sum of the expression from k=1 to k=3 substitute…

Q: 8s - 16 (s² + s)(s² + 1),

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Q: Let a, = 1 and a₁ + a1 = n² + 2n, n ≥2. Evaluate S

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Q: UIN (x − 1) − = (x + 2) = 7

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Q: (s-4) L-lis2-85-9). Find L-1

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Q: 15- (x + 5)lnxdx =? a) (-21/4) - 12In4 b)O (21/4) - 12ln2 (23/4) - 12ln4 d) O (-23/4) + 12ln2 e)…

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Q: 1 L [s² +2s+5)

A: Let's find.

Q: Solve for n if P(n,5)=120C(n,3)

A: The objective is to calculate the value of n, for which the following equation is…

Q: 2. S 2z+8 dz (z+7)a

A: A detailed solution is given below

Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: 16 If X-B (4, p) and P (X=0)=- then P (X=4) 81

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Q: 22.L{tsin (-2t)} O - (s²+4)? 2s (s² +4)° 8s 4s (s?+4)

A: Correct option is  = A Please find attachment for the details solution

Q: 5 -2s2-3s+4- L-¹1-

A: We will use Laplace transformation table to find inverse Laplace transformation of given function

Q: 2. The sum of three consecutive positive odd integers is always a multiple of (A) 3 (B)5 (C)7 (D)9…

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Q: 12 dx x3 - 2x -63X answer In (x -9) 3 I In Xt In (x+7) + C' 12 21 28

A: Solution:GIven∫12 dxx3-2x2-63xFormula:∫1xdx=log x+C

Q: O True (²7.¹7 (²77)) ²1¹7A (2)

A: This expression is False

Q: what are the first three terms in the binamial, expansion of (2a-0,5b) 1.

A: Given

Q: Find L S s²-48-7 Find L¹ 2s+6 s² +6s+34

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Q: 5 2 dr = dr- 0 (x²+9)½ /(6+zx) 0, 's (x²+9)½ * A) True B False

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Q: Prove that if n = nxn-1 holds integer value of -n, which means that for a positive integer value n,…

A: We have given that ddxxn=nxn-1 for any positive integer n. We need to show that, ddxx-n=-nx-n-1. We…

Q: 3 - 4 fX = the value of X" is - 1 %3D

A: We have to find the value of X^n

Q: 2 A= find For 3 -2 r B= 7 -1 O A +2B ®(A+2B) (AB)" 3)

A: NOTE: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Find (4t + 1)u(t-1)} e-5(55+4) s² a. b. C. d. O Ob OC Od 3e-s 5² S e $(5s + 1) s² e-5(55-4) 5²

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Q: 17. lim 12n+9 5n - 1 12

A: Consider the given limit  limn→∞5n-112n+9

Q: 13D 43. If a > 1 and b < 0, then 1-101 (A) (B) 1 9 (a) (D) b(a+1) (E)

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Q: – 3t +2 (b) 24 (a) 15

A: Here we can use the following formula: 1. Lafx+bgx=aLfx+bLgx2.  Ltn=n!sn+1

Q: 22. The expression (x-10)(x*) is equivalent to x". What is the value of n?

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Q: O d. 3 34 9x + 3 Which of the following expressions does not represent the sum: Select one: O a. 2k…

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Q: 14. If 3x + 1= 5, then x + (A) (B) 2 (C) 3 10 (D) 3 (E) 3 2/3

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Q: 1/2 z + 6 = 3/2 (z + 6)

A: We have to solve for the value of z in the above equation.

Q: 64. (r - 3s + t)(r - s + t)

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Q: 3/2+8(1)

A: Solve the expression as follows.

Q: 26. K(2人 +1)

A:

Q: an (b) Explain what it means to say that n=1

A: According to question,Given expression,∑n=1∞an = 12

Q: (2х — Зу)(4x? + 6ху + 9у?)

A: