For n is greater than or equal to  1, use mathematical induction to establish each of the following divisibility (a) 8 divides 5^(2n)+7.  [Hint: 5^(2(k+1)) + 7 = 5^(2) (5^(2k) + 7) +(7 - 52 · 7)]   b) 15 divides 2^(4n) - 1

Q: Use Mathematical induction to show that H sub(2^n) is less than or equal to 1 + n.

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Q: True or false: If n is a positive integer with d(n) = 6, then the only possible prime power…

A: n is a positive integer with dn=6.

Q: prove that is 11^k-4^k is divisible by 7    use mathematical induction

A: we have to show 11k - 4k  is divisible by 7 By using mathematical inductions.

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Q: Write a formal induction proof (Base Case and Inductive Step) Prove by induction that…

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Q: Use the Second Principle of Finite Induction to establish that for all n is greatre than or equal to…

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Q: Value of the 7th term in (2x + y)"?

A: Follow the procedure given below.

Q: I was asked to prove that 5^(2n+1) + 4^(2n+1) is divisible by 9 for all n that are positive…

A: SOLUTION-

Q: Find all integers n such that (n^2) - 1 is prime.

A: n² - 1 = (n-1)(n+1)  Now, if (n² - 1) needs to be a prime, then, either n-1 is equal to 1 or, n+1 is…

Q: Use induction to prove that 2*3^(n-1) is less than or equal to 2n choose n (picture attached)

A: We have to prove 2⋅3n−1≤2nn by using of principal of mathematical induction, where n≥0 Recall that…

Q: This will be (n+k-1)= 29+6-1 29 -¹1) = 34 29 = 278, 256.

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Q: Prove by induction that for positive integers n, 13|(4^(2n+1)+3^(n-1) )

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Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: Expand (4-x)^4 by using binomial expansion

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Q: Prove by induction that 11^n - 6 is divisible by 5 for all n greater than or equal to 1

A: Mathematical Induction :It is a mathematical technique used to prove the statement is true all…

Q: Find all whole#s that leave remainder 3 upon division by 5?

A: The solution is given below:

Q: Let k be any positive integer. Use induction to provethat for every integer n ≥ 0, k^(n+2) + (k +…

A: Given that  k be any positive integer. Use induction to prove that for every integer n ≥ 0, k^(n+2)…