Let P(n) be the statement that 1 +22+...+n n(n+1)(2n+1) = 6 (a) (1 point) What is...

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Let P(n) be the statement that 1² +22+...+n² n(n+1)(2n+1) = 6 (a) (1 point) What is the statement P(1). (b) (2 points) Show that P(1) is true, completing the basis step of the proof by mathematical induc- tion. (c) (2 points) What is the inductive step i.e., what is inductive hypothesis and what do you need to prove in the inductive step. (d) (2 points) Complete the proof of inductive step. for the positive integer n. 2. (5 points) Use mathematical induction to prove that 13 +23+ + n³ = (n(n+¹)) ² whenever n is a 2 positive integer. 3. (5 points) Use mathematical induction to prove that 2-2-7+2.7² +2(-7)= (1-(-7)"+1) whenever n is a nonnegative integer. 4. (6 points) Consider the series 1 2 1.2 2.3 + +...+ 1 n(n+1) (a) Find a formula by examining the values of this expression for small values of n. (b) Use mathematical induction to prove the formula you conjectured in part(a). Let P(n) be the statement that 1² +22+...+n² n(n+1)(2n+1) = 6 (a) (1 point) What is the statement P(1). (b) (2 points) Show that P(1) is true, completing the basis step of the proof by mathematical induc- tion. (c) (2 points) What is the inductive step i.e., what is inductive hypothesis and what do you need to prove in the inductive step. (d) (2 points) Complete the proof of inductive step. for the positive integer n. 2. (5 points) Use mathematical induction to prove that 13 +23+ + n³ = (n(n+¹)) ² whenever n is a 2 positive integer. 3. (5 points) Use mathematical induction to prove that 2-2-7+2.7² +2(-7)= (1-(-7)"+1) whenever n is a nonnegative integer. 4. (6 points) Consider the series 1 2 1.2 2.3 + +...+ 1 n(n+1) (a) Find a formula by examining the values of this expression for small values of n. (b) Use mathematical induction to prove the formula you conjectured in part(a).