5. (15) Use mathematical induction to prove that for every n E N the following is true. E2i – 27+1 – 1 i=0 (In other notation, 20 + 21 + 2² + 23 + . .. + 2" = 27+1 .- 1)

Q: 1² +2²+ •+n² = n(n+1)(2n+1) 6 for n EN

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

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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: Prove by induction. 3F, = Fn+2+ Fn-2 for n > 2

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Q: 4. Use mathematical induction to prove the truth of each of the following assertions for all n ≥ 1.…

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Q: Using mathematical induction, prove P(n) = 22n – 1 is divisible by 3 for every integer n > 1. Show…

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Q: 11. Prove that every positive integer n can be expressed in the form n=4k or n=4k+1 or n=4k+2 or…

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Q: Use Mathematical Induction to show that, for all n € Z†, 6 | (10″ + 2).

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Q: (4 – 2æ)".

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Q: 4. For n > 1, use mathematical induction to establish each of the following divisibility statements:…

A: let pn: 8/52n+7Base  step:For n=1∴52+7=25+7=32⇒8/32∴8/52n+7 for n=1∴p1 is true

Q: Use Mathematical Induction to Prove that 2 + 4 + 8 + 2 = 2(2" - 1)is true for any positive integer…

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Q: (d) Prove by induction that 5 "– 1 is divisible by 5 for all n e Z +.

A: we have to show that 5n-1 is divisible by 5 for all n belongs to Z+ by induction for n =1.

Q: Show that 1+5+9+...+ (4n-3) = 2n²n using mathematical. induction.

A: Base case:    For n = 1:          LHS = 1          RHS = 2.12 - 1 = 2 - 1 = 1      So, LHS = RHS.…

Q: Use induction to prove 12 + 22 + · . . + n² n(n+1)(2n+1) 6.

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Q: Prove the following fact by induction: For every non-negative integer n, 2 evenly divides n2 – 7n +…

A: Let the statement is P(n): 2 evenly divides n2 - 7n + 4. For n=1, n2 - 7n + 4 = -2 which is…

Q: Q6 Use mathematical induction to show that n > 2n +1 for all integers n > 2.

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Q: (1) Prove by induction: ₁(²- i+1)= n³+2n (2) Prove by induction: 1(1!) + 2(2!) + + n(n!) = (n + 1)!…

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Q: 2. 2 +3+5t t(2n-1)=h(2n-1s (2nt) %3D 3. for all nz I

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