Proof Induction by Peter Martin Jones

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Kindle Edition

33 pages


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Proof  by  Induction by Peter Martin Jones

Proof by Induction by Peter Martin Jones
| Kindle Edition | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 33 pages | ISBN: | 8.35 Mb

SynopsisThis series of booklets is designed to give a thorough grounding in Inductive Proof. A good understanding in this topic is essential for all those people who wish to go on and study Mathematics and other science subjects like, Physics,MoreSynopsisThis series of booklets is designed to give a thorough grounding in Inductive Proof. A good understanding in this topic is essential for all those people who wish to go on and study Mathematics and other science subjects like, Physics, Chemistry and Engineering.Often the fundamental concepts like these are frequently not completely understood leading to confusion and often dissatisfaction and can result in people giving up on the subject altogether.This is a shame because such confusion can often be attributed to poor teaching or unexplained misconceptions.

This series of booklets sets out to explain fully and clearly every step throughout with everything presented in an easy to understand format.There are a sufficient number of examples in this booklet to cover most types of questions that the student is likely to encounter.All booklets in this series are competitively pricedThis booklet is Proof by Induction IP1 in the series and contains the following topics:Prove that 1+2+3+ . . . + n = ½ n (n+1) where n ≥ 1Prove that for any integer n ≥ 1that:1+3+5 +. . .+ (2n-1) = n²Prove that for any integer n ≥ 1that:2+4+6+ .

. . +2n = n (1 + l) – n2Prove that n !≤ n² for any integer n≥1Prove that 2n > n2 for any integer n:n ≥ 5Prove that for n ≥ 1- 2n3 -3n2 + n + 31 ≥ 0Prove that 4n > n4 for any integer n >4Prove that 12+22+32 +. . . +n2 = n(n +1)(2n +1)/6 where n ≥1Prove that 13+23+33+ . . . +n3 = ¼ n2 (n+1)2 for n≥1Prove that 1⁄1.2+1⁄2.3+1⁄3.4+ . . .+ 1⁄n( n+1) = n⁄( n+1)Prove that 22+42+62+.

. .+(2n)2 = 2⁄3n(n+1)(2n+1)Prove that 1.4+2.5+3.6+ . . . +n(n+3) = n(n+1)(n+5) ⁄3Prove that 23+43+63+ . . .+ (2n)3 = 2n2(n+1)2 where n ≥1.Prove that 4 + 42 + 43 + . . . + 4n = 4⁄3 (4n – 1) Where n ≥ 1Prove that (2+3n) = n⁄2 (3n +7) where n ≥1Prove that 3 divides into 4n+5 where n ≥ 1Prove that n!>2n where n ≥ 4Prove that 23+43+63+.

. . +(2n)3 = 2n2(n+1)2 Where n ≥ 1Prove that – 1 +4 –8 + . . . +(–1)nn2 = 1⁄2 (–1)nn(n+1) Where n ≥ 1Prove that: (1– 1⁄22 )(1– 1⁄32) (1–1⁄42)



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