9. (a) Show that if n is an integer, then: -o3* (") = 4". %3D (b) Let n be a positive integer. Show that ()+ (") = } (). %3D n+1

Q: Select the function that is (nlogn) 1) 5n+17logn 2) 6nlogn+n¹1 + 2 3) 23nloglogn + 3nlogn 4)…

A:

Q: Q2) Use rounding to 6 digits and compute each of the following: a) P(0.01), where P(x) =…

A: Given, P(x)=(ex-1-x)x2 therefore, P(0.01)=(e0.01-1-0.01)0.012                                =…

Q: If X~N(2,9), compute a. P(X>=2) b. P(1<=X<7) c. P(-2.5<=X<=-1)

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

Q: of Easte 3 5² +45+13 ی ]

A: Some of the properties of inverse Laplace transformation are…

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

A:

Q: Q3\Find each the following: (1 2 3 4) 3. Order of (2 3)(6789). (A) (B) (C) (D) (246 8). Order of (1…

A:

Q: Determine the coefficient of at in (1 – 4a²)ó by completing the following given steps.

A: Concept:

Q: Find a formula for ¹ - 1²/ (²1) + 1² ( 2 ) -—- ... ₁ (2). (G) + (-) + I u

A:

Q: 8. Rewrite VVd*in exponential form.

A: dxmk=(dx)1mk              = dxmk             =dxm1k

Q: A0) = 2, A2) = 5 and f(n) = 2 An - 1) +3 (n - 2) + fAn - 3) for all n> 3. Find f(4).

A: Solution:

Q: (-1)"(36)" (2n)! Use a McLaurin's to find round your answer to four digits after the decimal sign.…

A: By using a MacLaurin's to find.

Q: Find the dual of the Boolean expression O T. (T+0). (+y+2) O a. (1.1). (* + y | 2) None of these OT.…

A:

Q: Find a number n e N such that 2" > 102000 and 2" has among its 2000 last digits at least 1000…

A: We will use logarithm to solve the problem

Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

Q: True or false: If a,b,m are integers with m > 0 satisfying m|(a^2 − b^2), then m |(a −b). Justify…

A: Given Information: If a,b, and m are integers satisfying m|a2-b2. To check: m |(a −b) for any…

Q: » (6)- (:) + (2) ---» :) - (3) n n +(-1)" (" ). = 0. с) + 3 n +...+n = n2"-1.

A:

Q: Find a formula for ¹ - 1²/ ( 7 ) + 3² ( 2 ) - ··· + + (−1)n. 2+1(1).

A:

Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

A:

Q: Which of the following sets is empty ? * O (x: X = x*2} O (x: x is not equal to x) O (x: x is not…

A: A set is said to be empty if it does not contain any element.

Q: Find a formula for +(−1)n. (2). 1 1 ¹ – ²2 ( ² ) + ² ( 2 ) - -· ··- 1 n+1

A: To Find: A formula for .

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A:

Q: 1- x**! 1- x n+1 6 (x # 1) r=0

A:

Q: .Findthefirst4termsineachsequences a) tn=3(-2)^n-1

A: Find the first four term

Q: suppose that X~N (3, oʻ), AP (3<X<6) =0.4, then P(X20)= A.0.4 B.0.9 C.0.6 D.0.1

A: We have to find given probability.

Q: (4x*) for all x#0? Show the manipulations that lead to your 5. Which of the following is equivalent…

A: Explanation of the answer is as follows

Q: 14) Show that f (æ) = -æ³ +2 is decreasing on the entire real number line. (Show Graph)

A: we have to show that the given function is decreasing and also draw the graph of f(x)

Q: For the following claim Below you must disprove it. "For all integers x, x^2 + 1 is odd" Use the…

A: for example take x=3 .  then x^2 +1=10 , which is even.

Q: Prove that if x is an even integer, thenx^2−6x+ 3is odd

A: Any integer of the form 2m+1 is odd.

Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

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: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: (4) For all natural numbers n, 4^n - 1 is a multiple of 3

A:

Q: Evaluate: (3 e + 9* – 7) dr =.

A: Given : ∫3e3x+9x-7dx

Q: prove that Every positive integer n can be written as n =( 2^a)(5^b)c, where c is not divisible by 2…

A: Fundamental Theorem of Arithmetic: Every positive integer (except n=1) can be uniquely expressed as…

Q: Evaluate 7x 11 √(x - - − 1)(x – 3) - - - dx

A:

Q: Let 43^(55) + 55^(43)= 7q+r, where q and r are two integers such that 0<=q<7. Then r is equal to?

A: Let 43^(55) + 55^(43) = 7q +r, where q and r are two integers such that 0&lt;=q&lt;7. Then find the…