Observe that 1 13 = 1 3 1 13 + 1 35 = 2 5 1 13 + 1 35 + 1 57 = 3 7 1 13 + 1 35 + 1 57 +

Chapter 5, Problem 3

(choose chapter or problem)

Observe that

\(\frac{1}{1 \cdot 3}=\frac{1}{3}\)

\(\frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}=\frac{2}{5}\)

\(\frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}=\frac{3}{7}\)

\(\frac{1}{1 \cdot 3}+\frac{1}{3 \cdot 5}+\frac{1}{5 \cdot 7}+\frac{1}{7 \cdot 9}=\frac{4}{9}\)

Guess a general formula and prove it by mathematical induction.

Text Transcription:

1 / 1 cdot 3 = 1 / 3

1 / 1 cdot 3 + 1 / 3 cdot 5 = 2 / 5

1 / 1  cdot 3 + 1 / 3 cdot 5 + 1 / 5 cdot 7 = 3 / 7