Solved: Prove that for all integers n 1, 1 3 = 1 + 3 5 + 7 = 1 + 3 + 5 7 + 9 + 11 = = 1
Chapter 5, Problem 28(choose chapter or problem)
Prove that for all integers n ≥ 1,
\(\frac{1}{3}=\frac{1+3}{5+7}=\frac{1+3+5}{7+9+11}=\cdots\)
\(=\frac{1+3+\cdots+(2 n-1)}{(2 n+1)+\cdots+(4 n-1)}\).
Text Transcription:
1 / 3 = 1+3 / 5+7 = 1+3+5 / 7+9+11 = cdots
= 1+3+ cdots + (2 n-1) / (2 n+1) + cdots + (4 n-1)
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