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.

Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.4: Least Common Denominators
Problem 13E
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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.
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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