4) Apply induction to show that 9' +9* 9(9" – 81) ,n 2 3. .+9" = 8.

Q: 1,319929 439= (は

A:

Q: Find LOVE LOVE 0 0 [Trysin(x² + y²) dady

A:

Q: find a Positive integern for which the equality holds %3D

A:

Q: Determine the number of coprimes of p5 below p for the cases p = 2,3,5 by listing them neatly. Also,…

A: The function counts the number of coprime integers less than n

Q: Consider the following statement. 9n<5^n   What is the smallest positive integer n for which the…

A:

Q: Using mathematical induction, prove P(n) = 2 x (2"-1 x 3" + 2) is divisible by 5 for every integer n…

A: To prove by mathematical induction  P(n)=2(2n-1×3n+2) is divisible by 5 for every n≥1.

Q: term

A:

Q: Drove: am t (att)" =1 +a(it()m=) Cmod acate) Where a, ore integers. n

A:

Q: 2 +3" En=D0 %3D 5n+1 Select one: O True O False 5/56

A:

Q: problem is from discrete math regarding profs my strong induction. If you can’t help, no worries,…

A:

Q: (b) Prove that any odd number is expressible in the form 4n + 1 or 4n + 3 where n is an integer.

A: Number System

Q: 4. Knowing that 1 + 3 + 5 + …+ (2n – 1) = n², find 1++3 +5 + .…+ 135 =

A: Solution :   Given that  1 + 3 + 5 + ... + (2n - 1) = n2    -----(1)

Q: 3.2÷.8=

A: In math, long division is a method used for dividing large numbers into groups or parts. It breaks…

Q: Prove the following using either direct proof, indirect proof, or proof by contradiction. 1. If n…

A:

Q: 2n 10. Prove that 31 (5 - 1) for every integer n 2 0.

A:

Q: Using mathematical induction, prove that the Binomial formula holds for complex numbers (²1 Ĺ (2₁…

A:

Q: 1) Write all the following as expansions : > 0.2 > V26 V35 (0.99)-4 V(4 – 2y)2 ,y<2 2х-1° 2

A: (a) 0.2answer(a)0.2=2100.2=15(b) (26)13 answer(b) using approximation to solve the cube rootput x=27…

Q: Jse mathematical induction to prove that for each integer n > 4, 7" > 6" + 200.

A: Mathematical Induction: Suppose P(n) be a mathematical statement. Then P(n) is true for all n≥m,…

Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: 2 4. Express 989 = 23 43 in the form x² + xy + 5y².

A: The given number is 989. The objective is to express the given number in the form of x2+xy+5y2.

Q: Expand the expression for Mr Taylor.

A: The previous solution is incorrect. Please follow this one.

Q: is 4= Sinh(2sinhix) shaw Hh at %3D 2 (a)

A:

Q: 1. Show that 2465 is a Carmichael number.

A:

Q: The first three terms in the expansion of (1 + ay)^n are 1, 12y, and 68y^2. Find a and n.

A:

Q: - 5. Prove that an integer n is odd if and only if n° – 3 is even.

A: Answer

Q: i. What is the P-value if the claim is modified to state that the proportion is equal to 0.5?

A: 2.i. In a study of smokers, after using nicotine patch therapy 39 were smoking one year after the…

Q: Prove E-1(4i – 3) = n(2n – 1) for natural numbers n 2 1. i=1

A:

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

A:

Q: 2) Prove that 4 divides 7" -3" for eachn EN

A:

Q: Find a formula for the general term a, {5, 8, 11, 14, 17, .} 5n + 3 On+3 O 3n + 2 O 2n + 3

A: We can answer the question as below

Q: (I + u)u] 2 induction prove that 13 + 23 + ...+ n³ = , for n > 1. 2.

A:

Q: Find the value of (1+ i)148 – (1 – i)'48 Do not just state the answer. Show your computations.

A:

Q: Give a combinatorial proof for the identity 1+2+3+..+n= (",").

A:

Q: Evaluate: (3 e + 9* – 7) dr =.

A: Given : ∫3e3x+9x-7dx

Q: Find residue 1 Res₂=0 24 +4% 2 Res 2 = 1 ze 3 2³-1 of

A:

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

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.