li'n -3Carl) lim -3n-3 ヘ→ 0 ヘう o

Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: Let X- N (8, 64), Find P ( 8< X< 16).

A: Standard normal distribution: The standard normal distribution is a special case of normal…

Q: |x+7/2| ≥ 9

A: Given,

Q: 5 y 4

A: The order of surd is indicates the index of root to be extracted. For example: n√(x) here n is…

Q: look for the pattern, solve for the value of X…

A: It is given that,…

Q: (f) The sum of the squares of the odd integers between 0 and 100.

A: Explained below

Q: For n = 10 and x = 7, find n! x!(n-x)!

A: The given expression is .To solve the expression for and .

Q: Find all integers n > 1 such that 1n − 1)" is +2+...+(n divisible by n.

A: To find all the integers n&gt;1 such that 1n+2n+...+n-1n is divisible by n

Q: Which is greater where n &gt; 8?

A:

Q: prove (1+ )" in <4 for all n21

A: In the given question we have to prove that  1+1nn&lt;4∀n≥1 . we can prove this by two methods one…

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

A:

Q: How did you found the bounds 2 and 8

A:

Q: Why is (subtracting two positive numbers that are each less than 1), less than or equal to (1 minus…

A: Since r and s are both between 0 and 1  Then 1-r is positive and also 1+s is positive  Now , take…

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

A:

Q: For X - N(8, 6²), what is P(16 < X < 20)?

A:

Q: 27 en+1 – 1 < 0.05 ? 2 (n + 1) · (n + 1)!

A: Given: The expression is, 272en+1-1n+1n+1!. Calculation: Obtain the value n such that…

Q: True or False: The summation 18+28+...+n8 is a polynomial of n of degree 8.

A: Given that the summation 18+28+...+n8. The objective is to check the statement " the summation…

Q: 3/4(8y-9)&lt;3

A: We multiply both sides by 4 first.

Q: Which of the following is true? Select one: a. (n+1)= n(n) for any real number b. г(n) = n(n+1) for…

A: The objective of the question is to determine which of the given mathematical statements is true.

Q: (c) Find the smallest integer n that satisfies 1.65">56.

A: Given, 1.65n &gt; 56 We can find n by applying log on both sides.

Q: What is P(3sX<10)? *

A: From the given probability mass function we find the probability.

Q: is 5 the sulotion for x+3<8

A: Given inequality x+3&lt;8 tells us that whatever be the solution the final value on Left hand side…

Q: Use Dirichlet's principle with n = 10 to find a rational approximation of T.

A:

Q: Can you elaborate more about 1-P(x<3) and 1-P(x</(equal)2).

A: We have given that λ = 2.4X ~ Poisson (λ)Formula: P(X = x ) = e-λλx/x!

Q: What is the least coefficient in the expansion of (x -1)7?

A: Use Pascal's Triangles to find least coefficient in the expansion of (x -1)7

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.