1.3 Mathematical Induction EXERCISES 1.3 1. Use mathematical induction to prove that each of the following identities ar

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1 3 Mathematical Induction Exercises 1 3 1 Use Mathematical Induction To Prove That Each Of The Following Identities Ar 1 (80.55 KiB) Viewed 70 times

1.3 Mathematical Induction EXERCISES 1.3 1. Use mathematical induction to prove that each of the following identities are valid for all n EN ..+ (m1) *b. 1 + 3 + 5 +.+ (2n - 1) = n* 2 nin + 1)2n + D) *c. F + 2 + d. 1+2+...+ = [na + 1)? 2 6 -e. 2 + 2 + 2 + ... + 2 = 2(2-1) E For X. E R ***--= (x - xXx" + xy + ... + x) 1 1 2(3) (n + 1) 2. Use mathematical induction to establish the following inequalities. .b. 2* > *' for all n E N. 25 *a. 2"> for all + EN d. 1' +2+...+*<for all n *ca! > 2 for all € N, n 24 11 2+1