Find the value of  n! (n − r)!  when n = 15 and r = 13.

Q: Why must nCr always be less than or equal to nPr for any given n and r

A: Permutations and combinations are given.

Q: (n!)²3" -(x)" Σ n = 1 (2n)!

A: Use ratio test for Radius of converges

Q: So dy y2+9' Evaluate 4. k/6

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Q: How many terms are needed to estimate 10+(-1)".n 5n (- to n=0 within 0.1? Justify your answer!

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Q: Solve the diffeventialequatio n : %3D

A: We have the differential equation y'=4yx . We need to solve this differential equation and find out…

Q: The equality 2+3=D3+2 shows that addition is associative. O True False Previous

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Q: Find by direct calculation. Find by conditioning on the sum of these two numbers.

A: Travellers living in Shenzhen depart 'm' persons daily to Hong Kong West kowloon Station On a…

Q: For n-1.2.3 the expression 4n+2 is a multiple of

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Q: Assume that n / 7 = q R3. What is (3n + 4) / 7

A: Givenn/7 = qR3n = 7qR3

Q: or n>3

A: Given: Mathematical statement 2Fn>Fn+1 for n>3. We have to check whether a given statement is…

Q: Find (s+2)e -AS 2 s² +2s+4 4{}

A: Properties of inverse Laplace transfomation…

Q: For how many values of n is the sum 1 + 2 + · • + n not divisible by n if 1 ≤ n < 100?

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Q: How was the S1 found on answer A?

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Q: -1) and n n(r

A: Limit of a sum:∫abf(x) dx=h→0limh[f(a)+f(a+h)+f(a+2h)+...+f(a+nh)+....+f(a+(n-1)h)]h=b-annh=b-a

Q: why

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

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Q: B. Solve for the indicated term of each expansion. 3. The term involving x* of (+52

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Q: (- 1)"x" Σ 6" (n² + 9) n=1 8.

A: Given

Q: Find the first 4 terms of n+3 n² +1

A:

Q: Solve for n. k (3-n) %3D

A: b=k(3-n)pbp=k(3-n)

Q: 2"-1 for positive integers n. 2n

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Q: How did they got n(n+1)(2n+1) / 6

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Q: b)+++ -1- for all n 1. ... 4 2"

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Q: Find the value of c if (1 + c)-n = 3 n = 2

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Q: Is it better to receive $1000 today or $1300 in 4 years? Consider r = 0.08 and r = 0.03.

A: Given: Is it better to receive $1000 today or $1300 in 4 years? Consider r = 0.08 and r = 0.03.

Q: b) Σe1(-1)n+1 3+n 5+n

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Q: Find the value of x that makes m || n. 7. eA (16x – 6)° x=_

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Q: What is the value of the 3rd term of the expansion (3y−2)^7?

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Q: -- ΣΧ E n² 22n n = 0 II

A: follow the next step

Q: 48) Σ- (-1)" n n n+1 (b) 2n=1 n2" 8.

A:

Q: п? +1 n- 2n2 +n – 1 n=2

A: Alternate series is convergent if  Terms of series are decreasing and limit of an as n -&gt;…

Q: Evaluate: n!/(n - r)! for n = 20 and r = 3.

A: It is given that, n!n-r! for n=20 and r=3.

Q: Find the value of $c$ if $\sum_{n=2}^{\infty}(1+c)^{-n}=2$

A: We have given;

Q: How many times does it take if u add 4+8 until you get the answer 40?

A: To find: The number times it take to add until get the answer 40. Calculation: Assume the number…

Q: Evaluate for n equals -2 n2+9n+3

A: The given expression is

Q: n2 when m 4 Evaluate 10m+ 5 and n = 4. %3D

A: Evaluate 10m+n24 when m=5 and n=4

Q: IF m*n DENOTES 2m – n², FIND THE VALUE OF: ii. -3 * V 5

A:

Q: 3. n2 + 7n + 10

A: The telescoping series ∑n=1∞3n2+7n+10

Q: Find the big O of the function ƒ(n) = n²" +n"

A: For (a), We are given the function f(x) = 3x2 - x - 1. We need to show that f(x) is O(x2) by finding…

Q: (-1)"+'(x + 2)" n2" n=1 8.

A: We have given a power series; The interval will be; So the interval is (-4,0)

Q: = (ª*,2 n(n+D2| 13 + ...+ n³

A: We will prove the game statement by using the principle of mathematical induction in which we show…

Q: Suppose that the number of employees in a new company is expected to grow, with the number of…

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Q: that you are using. Σ n=1 n/2+1 •a.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The S.D. of the first n odd integers is √85 , find n

A: Sum of first n odd numbers is given by: ∑ixi=n2 Sum squares of first n odd numbers is given by:…

Q: solve for n 6(n+5)=2

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Q: Q.5) (a) Evaluate L-! 2+6s+9 (3-1)(s-2)(s–4

A: First use partial fraction then take inverse laplace transform

Q: (-5)" n2 n- 1

A:

Q: Which of the following statements are true (as n gets large or n → 0)?

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