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

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

A:

Q: A poll of 220 students at a university reveals that 89 are taking a lab science course, and 57 are…

A: d) The explanation of this part is wrong. Note that P((L∩H)')=P(L'∪H') [using De-morgan's law]So the…

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

A:

Q: term

A:

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

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

A:

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: O True (²7.¹7 (²77)) ²1¹7A (2)

A: This expression is False

Q: Simplify 17. (n+ild (n-1)! 18. (3n+1)! (an)!

A: For expression 17:(n+1)⋅n For expression 18:3n+1Explanation:For expression 17:(n−1)!(n+1)!​We can…

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.