Using complete sentences. Use terms as seen from other image such as Suppose, We must prove, Consider, etc. For the next class, please practice mathematical induction by proving the following statement. I will collectthis at the beginning of class.Exercise. Prove that 1 2+2.3+3.4+...+n (n+ 1) = "lu+bi+2 for all integers rn > 1.n(n+1)(n+2)%3D luction to Mathematical Induction.pdf100%Since P(1) is true and P(k)Thus, P(k+ 1) is true (Follow the equalities and compare this with P(k+ 1)).implies P(k+ 1), we have P(n) is true for all z>1.One more example to help this sink in. It is not necessary to use the P(n) language. Instead, we refer toP(n) as "the statement."Result. Prove that 1+ 2+3+..+n2n+1) for all integers n 2 4.A Open iProof. For the base case, we show that the statement is true for n 4. The left side is 1+2+3+4 104(4+1)and the right side is10. so the statement is true for n= 4. Suppose the statement is true for someinteger k 2 4, that is, supposeA (k +1)1+2+3+ +k=(this is the induction hypothesis) We must prove that(k+1)((k+1)+1)1+2+3+..+ k+ (k+ 1)2(4 +1) (k+2)21ConsiderA(A+1)1+2+3+ * +k+ (A + 1)-+(+1)by the induction hypothesis. Simplifving (ue ll factor first)2.(A+1)A+2(A+1)(A-1)(This, the statennt is 1mie for all 2 4 bocause the stateneut is true for z-4and thhe statement is truefor k+1 whenever it is true forWhy 4 BECAUSE I FELT LIKE IT! ItLals wautel to startThe base case Was pved ForCommuents on this proof.ENDHOMEINSDELBACKSPACENUMLOCK&8

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For the next class, please practice mathematical induction by proving the following statement. I will collect this at the beginning of class. Exercise. Prove that 1 2+ 2-3+3-4+ +n (n+ 1) = "la+la+2 for all integers n 2.

For the next class, please practice mathematical induction by proving the following statement. I will collect this at the beginning of class. Exercise. Prove that 1 2+ 2-3+3-4+ +n (n+ 1) = "la+la+2 for all integers n 2.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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