Q1 & 2 step by step 1. Use proof by induction to prove that: r3 = -n² (n+1)?4r=12. Use proof by induction to prove that: r(r + 3) = – n(n+1)(n+5), ne R3r=113. Use induction to prove that: r(r +1) = -n(n +1)(n+ 2)3r=14. Prove that: (r-1)(3r – 2) = n² (n – 1) for all positive integers n.%3D|5. Prove that: r.r!= (n+1)! - 1 for all n > 1%3D6. Prove that 13" - 6h-2 is divisible by 7, n227. Prove that 26n - 32n-2 is divisible by 5.8. Given that f(n) = 24x 24n + 34n, Where n is a non - negative integer;a) Write down f (n+ 1)- f(n)b) Prove by induction that f (n) is divisible by 8.9. Prove by Mathematical induction that 52n-1 is divisible by 25 for all positive integers n22.2 12" 2"-110. If A =, prove that A =0 1111. Prove that every set withn elements has 2" subsets. (Show that the power set of the set of nelements is2").12. Prove by induction that n(n² + 2)is divisible by 3, where n is a positive integer.13. Use mathematical induction to prove that(cos0+isin 0)" = cos no +isin nº where 0 is a positive integer. (CGCEB)%3Dn²(n+1)?Prove by mathematical induction that rFind the sum of the cubes of the first n odd4СССЕВ)15. Prove by induction that 12Yr+1) = n(n+1)(n +2)(3n + 1) where n is a positive integer.Use mathematical induction to prove that (3r+r) = n(n+1)² where n is a positive integer.Frove by induction that for every positive integer, the integer 5t +3n-lis divisible by 9.

Name: Q1 & 2 step by step 1. Use proof by induction to prove that: r3 = -n²
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Q1 & 2 step by step 1. Use proof by induction to prove that: r3 = -n² (n+1)?4r=12. Use proof by induction to prove that: r(r + 3) = – n(n+1)(n+5), ne R3r=113. Use induction to prove that: r(r +1) = -n(n +1)(n+ 2)3r=14. Prove that: (r-1)(3r – 2) = n²