Prove the property of the Fibonacci numbers, F(n) = 5(n 4) + 3F(n-5), for n ≥6

Q: If n be positive integer, show that the algebraic sum of the numerical coefficients in the expansion…

A: As given above that n be a positive integer. And the given expression is: 3x-2yn We have to prove…

Q: Suppose A = {2, 5, 7, 9, 13, 25, 26}. (a) Find n(A). n(A) =  (b) True or false: 7  A True False…

A: Given: A = {2, 5, 7, 9, 13, 25, 26}. The event A contains the outcomes 2, 5, 7, 9, 13, 25, 26.

Q: (n+1)! (n-1)! = 10n

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Q: Is 18* 1/3= greater then 1/3 ?

A: Given : We have to check whether 18*1/3 is greater than 1/3

Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: Evaluate -2セ 34 L{+(e 2te

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Q: Consider all positive integers with 3 different digits. (Note that 0 cannot be the first digit.) (1)…

A: Iam assuming that the numbers from 0 to 99 are not valid because they are not 3 digit numbers, so it…

Q: What is the value of a after running the following R code? a <- 1:5 a <- (3*sum (a)) + 1

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Q: What are other similar expression patterns based on n(n+1)/2

A: Solution:-

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

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Q: How many 6-digit numbers have three even and three odd digits? (The first digit cannot be zero.)

A: It is given that a 6-digit number is to be formed which will have three even and three odd digits.…

Q: (9) VL1, L2 ((L1 UL2)* = (L2 UL1)*). True O False

A: Please check the next step for detailed solution

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: on the 4th implication where does the exponents of the i goes please elaborate

A: To find the rectangular form.

Q: What is the term involving a6 in (a² + ¹)1¹²? a

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Q: If A=-1 4 -3 -7/ -1 and A¹=/? ? (22 a ? What is the value of the element a? Give your answer…

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Q: hat is the last digit in the product of (3¹)(3²)(3³)(34)...(34⁰⁰)?

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Q: Write the following expression without using the factorial symbol (n-4)!/(n-1).    A.…

A: Known fact: n!=1×2×3×…×n-1×n

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

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Q: Can you compute (b) & (c) to 3 decimals?

A: The values of SST and SSR are 6,724.125 and 6,216.375 respectively. There are 10 observations.

Q: if (n+5)! = 56 (n+ 3)!, then (n+ 4)! = 5040 true O false

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Q: I also found that the expression was divisible by 13 at n=6 and n=10. Is there anyway you could…

A: Any number n can be written in the form          n = 3m, or 3m+1, or 3m + 2 for some integer m.…

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: What is the coefficient of x 9 in (x 3 + x) 5?

A: What is the coefficient of x9 in x3+x5.

Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: Obtain the regular expressions for the following: (a) {a4n+3 : n ≥ 0} (b) {a, a4, a8, … }

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Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

Q: For each positive integer n, define an = ((2+√3)" + (2-√3)") 2 It is known that an is a positive…

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Q: 5. From the 10 inflatable pool toys that you've bought during the past year, you plan to take 3 with…

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