) Write ‘There are infinitely many natural numbers n, such that 5n2 + 1 is a square number’ as a formal quantified statement. [Hint: You can express ‘infinitely many’ as ‘arbitrarily large’.]

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Q: 3. Show by mathematical induction that, for all n2 0, the equality +++.+ = 2 – +2 holds. ... 2Th

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Q: Prove the following statement: for all integers n> 1 1³ +2³+ 2 = [ n(n+1)]² 2 + n³ = [ 3

A: To Prove: The following statement: for all integers n≥1 13+23+...+n3=nn+122

Q: (a) Prove that for every integer n ≥ 2, 1 n+2 1 + n+1 +...+ 2n

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Q: 16. Use mathematical induction to prove that, for all natural numbers n, n [n(n+1) i=1

A: Prnciple of mathrmatimat induction:Alogrithm              1. obtained  P(n) and understand its…

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Q: Let P(n) be the statement that 1² +2²+...+ n² = n(n+ 1)(2n + 1)/6 for the positive integer n. a)…

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A: We will prove this by principle of mathematical induction.

Q: 7- Prove that for every positive integer n, 1.2.3 +2.3.4+ + n(n + 1)(n + 2) = n(n + 1)(n + 2) (n +…

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