Mathematical Induction Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Use mathematical induction to prove that whenever is a positive integer.

(2) Conjecture a formula for the sum of the first even positive integers. Prove your result using mathematical induction.

(3) Use mathematical induction to prove that for every positive integer

(4) Use mathematical induction to prove that for every positive integer

(5) Use mathematical induction to prove that for every positive integer

(6) Use mathematical induction to prove that for every positive integer

(7) Use mathematical induction to prove that for every positive integer

(8) Show that any amount of postage that is an integer number of cents greater than 53 cents can be formed using just 7-cent and 10-cent stamps.

(9) Use mathematical induction to prove that is a factor of where and are variables.

(10) Use mathematical induction to prove that for

(11) Use mathematical induction to prove that for

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