4 E (k +1)! 4. k=2 (n+2)! 5. (п-1)!

Q: 4 The value of 2 n=1 3n2 will be + 6n .... .

A: See solution below

Q: what is 2t+4s if t=5 and s=3

A: The given expression is 2t+4s.

Q: use the Principle of Mathematical Induction to show that the given statement is true for all natural…

A: To Prove: 12+22+32+...+n2=nn+12n+16

Q: 10. f(1) = –0.5 and f(n) = f(n – 1) – 0.5 for n>2 %3D - -

A:

Q: Suppose Z∼N(0,1). Then P(2 ≤ Z ≤ 3) is the same as

A:

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: (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: For this problem, assume the box contains 6 red balls, 7 blue balls, and 5 white balls, and that we…

A: Given that  box contains 6 red balls, 7 blue balls, and 5 white balls. Total number of balls is…

Q: Q1 (a) Calculate the coefficient of æ'yz in (r+y+2)13. (b) In her discrete math class, Karen was…

A:

Q: 3 E in (1 -) -in2 , . =-In2 =1 k2 –1 k=2

A: We will  use the limit of partial sum

Q: :""n e Z*, if n³ = 3k for some k E Z, then n = 3q for some q E Z." %| %3D

A:

Q: (d) For k satisfying -8 < k < k + 4 < 8, compute P(k < X < k + 4). (Round your answer to two decimal…

A:

Q: In(1 + s) - Σ-1 , for |2| < 1 because n +1 E(-1)*z* for |2|< 1. R=0 R=0 True False

A: From the given series we have to solve true/false problem.

Q: 7. 7. Suppose X - N(u.4), which is true?( X- (A) N(0.1): (B) PIX S0} = 4 (C) PIX-u>2; =1-0(1): (D)…

A: Here we use the properties of normal distribution to solve this problem.

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: ( a) Σ-1)t1, n+1 Vn² + 1 n² + 4 n=2 (b) (-1)" n(In n)³ n=2

A:

Q: BELL RINGER 1. V2k2 - 9 - x = 0 If k>0 and x=3 in the equation abové, what is k?

A:

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)

A:

Q: (-1)" -Σ S. n=1 Vn+1

A:

Q: 1 n +1 k=0 n n(n+1) 2 2 k=0 n 3 E k2 n(n+1)(2n+1) 6 k=0

A: Note: Since you have posted a question with multiple subparts, we will solve the first three…

Q: 2. Prove that, for all k E N, 2 can be written as the sum of two squares.

A:

Q: 2. If X is N(3, o² = 4) find (a) P(X < 3). (b) P(X <5), (c) P(X < 1).

A: Given that X is Nμ=3, σ2=4 i.e. X~N(μ=3,σ=2) Then Z=X-μσ follows standard normal distribution i.e.…

Q: 9. E (-1)* "´x" 2" 10. n=1 brex" 11. Σ (-1)" 4" In n 12. n=2 onul nsa (-3)" 00 13. У

A: Radius and interval of convergence

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: 14. If n e Z, then 5n2 +3n + 7 is odd. (Try cases.)

A: By method of direct proof, prove the statement " If n∈ℤ, then 5n2+3n+7is odd"k∈ℤk∈ℤ as follows.

Q: 1. s(z) = -4z³ In(z)

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: that for n > k we Sn+1 ||

A: The expression given is ,  n+1k+1=∑j=knnn-jjk The number of ways to partition n+1 objects into k+1…

Q: If Z~N(0,1), then what is Pr(-0.09 < Z < 2.54)? You can use Excel. Enter your answer as a decimal…

A: We have to find given probability

Q: Q3) IF N=[9; 8; 6; 5; 4] find 1- G=length(N) 2- C=N; 3- max (C) 4- min (N) 5- T=C+N

A:

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

A:

Q: Let S = { 1 - (-¹)" | n € N}. Determine inf S and sup S. Justify. n

A:

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

A:

Q: 4 The value of 3n2 will be + 6n .... n=1

A: We use partial fraction method to find the required sum of the series.

Q: 22. 5n2 + 35 = 0 23. 2m2 + 10 = 0 24.4m2 + 76 = 0 25. -2m2 -6 = 0 raw-Hill Companies, Inc.

A:

Q: Suppose O1 is twice as likely as O4, O1 is equally as likely as O2, O5 is 5 times as likely as O2,…

A:

Q: (15 49)} = at* e²¹ sen(71), et 2-¹ {-98 (8-2)² +49)} = What's the value of a*c?

A:

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

A:

Q: The average pollen count in a certain city on day x of the pollen season is P(x) = 6x − 0.2x2  (for…

A:

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

A:

Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

A:

Q: 1. For an = 5n2 + 9n3 + 1, an = n2, prove or disprove: rn = O(an) (n → o)?

A: We will use the standard definition.

Q: (エ+1)n n=D1

A:

Q: 8) F(s)=³-ks² 2 Ans. f(1) =2(e"-1)-! k

A: Solve the following

Q: 8. Prove 3n e R|n? – n < 0

A:

Q: (2). By Contrapositive: “V n e Z, if 3| (n² + 1), then 3 ł (2n² + 1)."

A: Solution:

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 s(n)=3n2−3n+5s(n)=3n2−3n+5, then s(n)=2s(n−1)−s(n−2)+cs(n)=2s(n−1)−s(n−2)+c for all integers…

A: Function represents the relation between dependent variable and independent variable. Function…

Q: 5x + 1 If y = then y' will be %3D 2x-1 – In 7' 5(2x** – In 7) – (Sx + 1)+) A. (2x- – In 7)2 5(2x-' –…

A: Given y = 5x + 12x-1 - ln 7

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.