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I that i i = Recall that n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 + 4 + · + 2n. Express your final answer as a simplified fraction involving n. (b) Use induction to prove your formula in (a). (c) Use (a) to find and prove a formula for 1+3+5++ (2n-1). Express your final answer as a simplified fraction involving n. (d) Use induction to prove your formula in (c).

I that i i = Recall that n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 + 4 + · + 2n. Express your final answer as a simplified fraction involving n. (b) Use induction to prove your formula in (a). (c) Use (a) to find and prove a formula for 1+3+5++ (2n-1). Express your final answer as a simplified fraction involving n. (d) Use induction to prove your formula in (c).

Advanced Engineering Mathematics
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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Recall that 12 i = n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 +4+· answer as a simplified fraction involving n. (b) Use induction to prove your formula in (a). (c) Use (a) to find and prove a formula for 1+3+5+ · + (2n-1). Express your final answer as a simplified fraction involving n. (d) Use induction to prove your formula in (c). ... +2n. Express your final
Transcribed Image Text:Recall that 12 i = n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 +4+· answer as a simplified fraction involving n. (b) Use induction to prove your formula in (a). (c) Use (a) to find and prove a formula for 1+3+5+ · + (2n-1). Express your final answer as a simplified fraction involving n. (d) Use induction to prove your formula in (c). ... +2n. Express your final
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