Recall that 72 i = n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 +4+ 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). + 2n.
Recall that 72 i = n(n+1) 2 (a) Use the above formula (not induction) to find and prove a formula for 2 +4+ 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). + 2n.
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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Transcribed Image Text:Recall that
72
i =
n(n+1)
2
(a) Use the above formula (not induction) to find and prove a formula for 2 +4 +
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).
+ 2n.
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