Let's consider sum 1+3+5+...+ (2n-1). (a) Obtain a formula for this sum experimentally by considering small...

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Let's consider sum 1+3+5+...+ (2n-1). (a) Obtain a formula for this sum experimentally by considering small values of n. (b) Use mathematical induction to prove the formula conjectured in the previous part. Make sure to clearly identify the base step, the inductive step, the inductive hypothesis, and where you use the inductive hypothesis. (c) (ON A SEPARATE SHEET) We have Theorem j=1 n(n+1) 2 Write conjecture from (a) using the summation notation, use this Theorem and summation manipulation to prove the formula. Let's consider sum 1+3+5+...+ (2n-1). (a) Obtain a formula for this sum experimentally by considering small values of n. (b) Use mathematical induction to prove the formula conjectured in the previous part. Make sure to clearly identify the base step, the inductive step, the inductive hypothesis, and where you use the inductive hypothesis. (c) (ON A SEPARATE SHEET) We have Theorem j=1 n(n+1) 2 Write conjecture from (a) using the summation notation, use this Theorem and summation manipulation to prove the formula.