Question 5 If a > -1 is real, prove Bernoulli's inequality: for n > 1, (1+a)" > 1+ na. Hint: use induction

Q: 3. Intro To Real Analysis

A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

Q: Fn+1 Fr-1 Show that A"; 3. Let Fn denote the nth Fibonacci number. Let A = (Hint: use induction).

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

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Q: 4. Prove the following by mathematical induction. η Σ i=1 = n(n + 1)(2n + 1) 6

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Q: (e) Show that every n ≥ 8 can be written as 3a+5b for some a, b € N.

A: Part e asked and answered.

Q: Use induction to prove that (2n + 1)² – 1 is divisible by 8 for each positive integer n.

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Q: Use Parseval's equality to show that 776 960 = n=1 1 (2n-1)6*

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Q: Prove using Mathematical n(n+1) Induction: 1+2+3+..+n= 2

A: Solving the problem by mathematical induction.

Q: Prove by induction Ein (-i)i ;2= (-1)" n(n+1) i=o 2

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Q: Question 4 Prove the following inequality using mathematical induction: 2n >n² for all positive…

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Q: Let n ≥ 1, x be a real number, and x ≥ −1. Prove the following statement using mathematical…

A: The principle of mathematical induction is a technique or method that is used to prove the statement…