Let Pin) be a statement 12 +22 + 32 + . +n? = n(n +1)(2n+1) for n>0. %3D ... 6. The statement Pa) is O A. It does not exist O B. n=1 OC 2- 1(1+1)(2 +1) 6. OD.02- 0(0 + 1)(0+1) %3D

Q: Which of the following is equivalent to (13a b)²a*? 3 A 1362 169a b2 13a b? 169a20b2 169a b

A:

Q: Let n EU = Z and p(n): n² + n is an even integer. a. Write the following statement: (Vn) p(n). b. Is…

A: (a) Here, the given statement is: For ∀n∈U=ℤ, p(n):n2+n is an even integer.

Q: verify (1-1) and that (1-1)(1)- a. Verify

A:

Q: 3. Integer Representation (48)10 = D16 (67)8 = C D10 = C D16 (4F)16 = C D10

A: For  (48)10 Hence (48)10 = (110000)2 = (60)8 = (30)16

Q: (QuestionID:T1Q2.4) What is the coefficient of 2° in the binomial expansion of (2² – 1)5 ? Choose…

A: What is the coefficient of x3 in the binomial expansion of (x2-1)5

Q: Q1 (b): If Xi= 1,3,5,7,9,11 and Yi= 0,2,4,6,8,10. The values of the :following term is i=n 2n – 3…

A: Given,∑i=1i=n2n-3πyi-11+xii-1here n=6

Q: +6n +3 is Θ (n)

A: 1st expression is TRUE

Q: (6.1) Prove if r is a positive, even integer then 10* – 1 is divisible by 11. (6.2) Prove if r is a…

A:

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: let a=2+7i b=4-2i Choose the correct result of a/b*

A:

Q: Find the quotient. x - 3x 4x – 16" x - 7x+ 12 -5x 4 -3.x+ 3 x+ 4 O 5 4.x * 3 x 4 O 4 3. x * 0, x *…

A: Given that: -5x4x-16÷x2-3xx2-7x+12 Now, x2-7x+12=x2-4x-3x+12=xx-4-3x-4=x-4x-3. Therefore,…

Q: Determine the correct expression for L{6u(t+2)+&e4t – 58(t) Oa. 5 8-4 O b. be-2 - 5e- 8-4 6e2s - 5e-…

A:

Q: S- xp

A: Given : ∫x2x2-a232 dx To find : Evaluate the given integral.

Q: prone 2 + 4 + 6 + + 2n = n(n+1). for every nz 2.

A:

Q: $(7n) = (n) if 7 divides n and 7. 70(n) if 7 divides n and 60(n) if 7 does not divide n (n) if 7…

A:

Q: Show that the following identities hold.

A: The two given identities are…

Q: Show that: 15|(24n − 1) for all natural numbers n.

A:

Q: Use Parseval's equality to show that 776 960 = n=1 1 (2n-1)6*

A:

Q: Question: Evaluate each following expressions a.) If x =0   evaluate 4x**2 + 5(9 +x) + x **5 b.)…

A:

Q: 2b -126 +4 factors to (36+2). O True O False

A: Consider the statement 8b2-12b+4  factors to 3b+22

Q: Ex:@ write out the expessicn în full- dummy indices 9 Hownany summakins aue theie y R (n=4) jki…

A: First we write expression of curvature tensor

Q: - Show that an = is monotone. n+2n+7 "}= •

A:

Q: Give a recursive definition for the following. (c) and (d)

A: In this question, concept of recursive function is applied. Recursive Function A recursive function…

Q: п n 9. Using the Binomial Theorem, show that Σ = n 2"-1. k k=0

A: We need to show that- ∑k=0nknk = n2n-1

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: b. For each positive integer n, let P(n) be the property 5* – 1 is divisible by 4. i. Write P(0). Is…

A: Given ,  For each positive integer n , let p(n) be the property 5n - 1 is divisible by 4