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)! (k-1)!(n-k-2)!

Q: n 2n + 2 /2 n 2n k k=1 \k –1, п+1 n -

A: The objective is to prove that ∑k=1nnknk-1=2n+2n+1/2-2nn This theorem can be proved by induction,…

Q: Find P (-1.5 < or equal to Z < 0.2) where Z ~ N (0,1)

A: We will use Standard Normal table to find the required probability.

Q: solve xy' - y = xkyn, 1) y¹ – O a. (k+n O b. (k+n O c. (k+n O d. (k+n - - n 1) x¹ - n - 1) x¹ − n 1)…

A:

Q: 3Fn - F n-2= Fn+2 for n>3

A:

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: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

A:

Q: b 2x 1! + 5x 2! + .+ (nt + 1)п! %3D п(п + 1)! + 10 x 3! + .. 2 3 + .. 1 n 1 + + + = 1 - 2! 3! 4! (п…

A: (b) Case 1 : n=1 2×1!+5×2!+10×3!+...+(12+1)1! = 1(1+1)!2×1! = 1(2)!2 = 2 Therefore, the result is…

Q: 8. If y = (x³ + 2x²)e2* determine an expansion for y(5). [y(5) = e2*2*(2x³ + 19x² + 50x + 35)]

A:

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: k+4 n(3n +7) k(k +1)(k + 2) 2(n+1)(n+2) k=1

A: Given ∑k=1nk+4k(k+1)(k+2) To show  ∑k=1nk+4k(k+1)(k+2)=n(3n+7)2(n+1)(n+2)

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)"…

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: write down the first five terms of each sequence

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: n-1 n-1 k n-2 n-2 - = P k X6n-10 X6n-9 = 4 - n-1 п-1 n-1 h k k n-1 X'6n-8 = r X'6n-7 = P h - . k - 4…

A:

Q: Expand 1/(z2-3z+2) in the region Mode z greater than 2.

A: Given: 1z2-3z+2, where z&gt;2 Calculation: 1z2-3z+2=1z-1z-2                   =1z-2-1z-1…

Q: in n k k-1 k (n+1\ \k-1) D+1 k+1 Pn+1 k

A:

Q: (Зп+5 Find infimum of A |n E N} n+9

A:

Q: Identify the two series that are the same.

A: In order identify the same series, just write the few terms of the gives series as follows. (a)…

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

A: Answer

Q: Fix k, n E N with n > 2 and k <n – 2. Prove that: | )-(".) · ) (:) ) (^) = (":") 2 + k 2 n – 2 n n +…

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: -ges 3n +n 9n b) L7-2)n+1n n! n=1 (-10)" d) 242n+1(n+1) n2 (2n – 1)! n=1 0=

A:

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: 3 – 1 х — 6 f(x) = - Where are the critical numbers? (Separate multiple answers with commas.) X =

A:

Q: 3)If X(z)= 2²-0-5z z²+0-75z+ b) X(n) = [4"-3"]u(n) c)) X(n) = [4¹-3"]u(n) . † 4) If X(2)(z-30)(2-40)…

A:

Q: OA -0 45x + 30 27, 73 absences; Yes, it is reasonable. O B. =0 45x-30.27; 12 absences; No, it is not…

A: Answer:

Q: 2n zn こ (n) n:0

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

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: 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: Зп + 1, A) 2n 4 — 2п n=1 n1-3n В) 42n n=0 (-5)1+2n C) 25п-3 n=4

A: Here we apply different tests like comparison test and Leibniz test.

Q: Do 4,5,6

A: solution

Q: 1.); 'n+1 2.1)n+1 (-1)n+1 n! (2х)^-1 3.) '(2n-1)5 4.)1)"-1 n+1

A: a) 1/2,1/3,1/4 b)2/3,3/5,4/5 c)1,2,3 d)6/9,7/11,9/12

Q: n=1 B. E(-1)"- In n n=2 1 Inn c.(-1)"+1. n- Inn (-1)*+1. n + n=1 E.(-1)" sin(n) n=1 E(-1)"- n=2…

A: This is a problem of series calculation. based on the several available tests we can determine which…

Q: Identify the two series that are the same.

A: We have to find which series are same. We have given series…

Q: 4n + 7 Σ (i) (ї) Z(n² – 8n + 16) 5n n=1 n=5 8

A:

Q: Show by two methods one algebraic and one combinatorial that: ΣΗ (E) (-) = (m*") -k=0

A:

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

A:

Q: 1 Σ1 п+1 k=0 n 2 Σ п(п+1) 2 k=0 n 3 Σ п(п+1)(2п+1) k=0 n Σ 3 n²(n+1)² 4 4. k=0

A: “Since you have posted a question with multiple sub-parts, we will solve first four sub-parts for…

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: 2 n n Σ (2n – 1 п — 1, =n k k=1

A: we have to prove that                                                we know that…

Q: ¸1(1 + r)n−¹ − 1. (n-1-1₁ r Sn (1+r)"So - P[- =

A: Sn = 1+rnS0 - P1+rn-1-1rAim: To find expression for 'n'.…

Q: [1 1 1 If A = 1 1 3"-1 3"-1 3"-1 prove that A" =| 3"-1 %3D 1 1 3"-1 for 1 3"-1 all values of n e N.…

A:

Q: [1 4 -1 2 -5. Find det(XYX-1). 0 -1. 7 8 Q2) If X = |5.5 -V2 4 2

A: det(A-1) = 1 / det(A)

Q: 2 P2(x) = 7 .2 =17 9. - - 2 2 9. P3(x) =|7 – 2 - 2 7 7 2 9. + 24 9. PA(x) = - - | 2 [72] Pn(x) =…

A:

Q: 2) 2 = п-1 n-2 3) 3. 4) = x+5 X-2 3 -4 5-t 13 5) 3+t |3D 12 n+8 n-3 6) -5 -1 II

A: We have to solve the equations for the x.

Q: h[n] = -8[n +1] + 8[n] + 28[n- 1] * x[n] = 8[n+ 1] + 28[n] + 8[n- 1] %3D - Find output vlnl = x[n] +…

A: Please find step by step solution below:

Q: Therefore n-1 ( fsi+4P + föi+3h foi+3P + fei+2h ) (foi-19+ fei-2k , feiq + fei-1k Tên-3 = k| i=0…

A: Given : In Theorem 4,                 fmm=-1∞=1, 0, 1, 1, 2, 3, 5, 8, ......... We need to explain…

Q: 1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

A:

Q: 8. Working over R, suppose that M = PDP ' where P 1 Then, for any positive integer k, we have that…

A: To find Mk =?

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…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.