Let n> 1. Prove by mathematical induction that 21|(4"+1 + 52n-1).

Q: Let denote the n-th prime number. Show that Pn Pn n=1 diverges.

A: Divergence of the series

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

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Q: Prove by induction that 7 divides 3^(5n+3) + 5^n for every non-negative integer n.

A: We can prove it by using mathematical induction.

Q: 7. Use induction to prove Bernoulli's inequality: If 1 + x>0, then (1+ x)" al+ nx for all natural…

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Q: n2 +2 2 3n for n = 1,2,3,.

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Q: () Prove by induction that for any positive integer n, n(n +1)(2n + 1) j=1

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Q: 2) induction to that for all Use prove nonnes atine integers 1, 51 (n=-n)

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Q: Use induction to prove that 5|(8" – 3") for all n E N.

A: Use induction to prove that 5/8n-3n for all n∈ℕ.

Q: 5. Prove by induction that for positive integers n, E-1(3i² + 2i + 5) = ÷(2n² + 5n² + 13n).

A: Given statement is : ∑i=1n(3i2+2i+5)=12(2n3+5n2+13n) Step1: Let us check if or not the given…

Q: Jse strong induction to prove that if n E N and n > 10,

A: Base step for Strong induction

Q: Suppose that you have 3 and 8 cent stamps, how much postage can you create using these stamps? Prove…

A: We shall show that every postage >=14 can be created using 3 and 8 cent stamps. And then deduce…

Q: use the mathematical induction to prove : 2" < n! < 3" , Vn E N* ,n 2 4

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Q: Use generalized induction to prove the given statement.   2n &lt; n ! for all integers n &gt; 4

A: To prove: The inequality 2n&lt;n! for all integer n&gt;4. Proof: Assume Pn be 2n&lt;n!. Basic step…

Q: Use mathematical induction to prove и исин) {i= VEN 2 1 = 1

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Q: Use Mathematical Induction to show that 512|8 · 5" + 6 · 32n – 80n – 14 - for all n E N

A: Solution

Q: Use mathematical induction to prove that: 3n 22n + 1 for n ≥ 1

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Q: Use mathematical induction to prove that: 3n ≥ 2n + 1 for n ≥ 1 discrete math

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Q: Prove by simple induction on n that 2" > n 5.

A: Note: First we will prove that the statement is true for n=1. Then we have to prove that the…

Q: 69. Use the principle of mathematical induction to prove that dk : (In x) = (–1)k-1 «– D! for k > 1.…

A: Use the principal  induction to prove thatdkdxk(ln x)=(-1)k-1(k-1)!xk , for k≥1.

Q: Use Mathematical Induction to prove that for n > 1, n²(n+1)? No other method of proof is acceptable.…

A: We have to prove ∑i=1ni3=n2n+124 by using principal of mathematical induction. First check for  n=1…

Q: By Principle of Mathematical Induction prove 6n 6

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Q: Please use regular induction to prove: 8|(9n + 7) for all n ∈ N

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Q: 7. Prove by induction that E,(-1)² = (-1)"n(n + 1)/2 for all n > 1.

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Q: Q2. Use induction to prove that for any natural number n , 2-1 = 2 – 2-".

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Q: Prove the following using mathematical induction. 3n+1-3 for all neN. 2 i=1

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Q: 2. Prove using induction that the following inequality holds for n2 0: (1+)"21+ n

A: First we show this is true for n=0,1 . Then we assume this is true for n=m , and we shall show this…

Q: A shop gives gift cards in nominal 25 and 40k. determine the possible total amount that can be…

A: Proof at first, the amounts seem semi-random:

Q: Use the principle of m matical induction to prove that for every positive integer n, the quantity…

A: Principle of mathematical induction: This method is used to prove a statement or theorem. In this,…

Q: use the mathematical induction to prove : H) 52n – 1 divided by 24, Vn EN

A: We have to prove by mathematical induction, ''52n-1 divided by 24, ∀n∈N.

Q: Use induction to prove that for all integers n > 1. n Σ+1 = η n+1

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Q: 4. Use induction to prove that 64 divides 32n+2 + 56n + 55 for every positive integer n.

A: Given: 32n+2+56n+55, where n is positive integer. To prove: 64 divides 32n+2+56n+55.

Q: Let k be a positive integer. Prove ÷VE. Note: do not use induction. j=1

A: The solution are next step

Q: Suppose a1 = 1 and a, = 2a,-1 - 1. for n > 1. Prove, using induction, that an 1 for all n. %3D

A: Given: a1=1 and  an=2an-1-1  for n&gt;1  Then we have to prove that an=1  for all n by using…

Q: Prove (by induction): n &gt; 0 for all n's in the naturals.

A: In a proof by induction, assume that n=k is true then, if n+k is also true  then the statement is…

Q: Use induction to prove: for any integer n > 1, (6j- 4) = 3n“ – n. j=1

A: We shall prove the given sum using Principle of Mathematical induction which means that a ) first we…

Q: Use mathematical induction to show that n > 2n +1 for all integers n > 2.

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Q: Use mathematical induction to show that, Vn > 3, 2n² + 1 > 5n.

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Q: Prove by induction that for every integer n 2 1, (xe2*) = 2"-1(2x + n)e", ne Z

A: We prove this by Mathematical induction

Q: Use mathmatical induction to prove that for all intergers n is greater than or equal to 1.…

A: For n = 1,       LHS = 4 [only 1 term]      RHS = 2.12 + 2.1 = 2.1 + 2.1 = 4 Hence, LHS = RHS.  So,…

Q: Use mathematical induction to prove that 1+5+9+...+ (4n – 3) = 2n². - N

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Q: Use the Principle of Mathematical Induction to prove that 2n< n! if n is an integer greater than 4.

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Q: Σ- n+ 1) (2n + 1), n2 1 i=1

A: Induction method says that if n=1is true then assume that n=k then prove that the statement is true…

Q: Prove by induction that for positive integers n:  4|(5^(n+1)+ 3^(2n-1)).

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Q: Prove by the method of Mathematical Induction that, E 2' = 2" – 1 for any positive integer n.

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Q: prove using mathematical induction that for all n ≥ 1 1+5+9+13....+(4n-3)=2n² -n

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Q: Prove the following using mathematical induction. Šr- n(n+1)(2n+ 6. 1. for all neN.

A: Question 1 solved ,pls ask other question in next turn

Q: Use mathematical induction to prove that:   3n ≥ 2n + 1 for n ≥ 1

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Q: Prove by induction that for any integer n: n(n+1) Σ; 2 j=1

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Q: By Principle of Mathematical Induction, prove 21+ 22+ ... 2" = 2n+1-2 for all n>1 %3D

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