Show that 1- 3 -1 1- 3 -2 1- 3 -4 1- 3 -8 - 1- 3 - 2 n - 3 2 1- 3 - 2 n -1

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Integration by Parts

Show that 1...

Question

Show that $(1 + 3^{- 1}) (1 + 3^{- 2}) (1 + 3^{- 4}) (1 + 3^{- 8}) . . . (1 + 3^{- 2^{n}}) = \frac{3}{2} (1 - 3^{- 2^{n} + 1})$

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\frac{3}{1 \cdot 2} (\frac{1}{2}) + \frac{4}{2 \cdot 3} {(\frac{1}{2})}^{2} + \frac{5}{3 \cdot 4} {(\frac{1}{2})}^{3} + \dots

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$(1 + \frac{3}{1}) (1 + \frac{5}{4}) (1 + \frac{7}{9}) \dots (1 + \frac{(2 n + 1)}{n^{2}}) = (n + 1)^{2}$

(1 + \frac{3}{1}) (1 + \frac{5}{4}) (1 + \frac{7}{9}) . . . (1 + \frac{(2 n + 1)}{n^{2}}) = {a (n + 1)}^{2}

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