Question

Đã trả lời bởi chuyên gia

Answer 1

a)

$S = 2 + 2^{3} + 2^{5} + . . . + 2^{51} \Rightarrow 4 S = 2^{3} + 2^{5} + 2^{7} + . . . + 2^{53} \Rightarrow 4 S - S = 2^{3} + 2^{5} + 2^{7} + . . . + 2^{53} - 2 - 2^{3} - 2^{5} - . . . - 2^{51} \Leftrightarrow 3 S = 2^{53} - 2 \Leftrightarrow S = \frac{2^{53} - 2}{3} b, S = \frac{1}{3} + {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + . . . + {(\frac{1}{3})}^{99} \frac{1}{9} S = {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + {(\frac{1}{3})}^{7} + . . . + {(\frac{1}{3})}^{101} \frac{1}{9} S - S = {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + {(\frac{1}{3})}^{7} + . . . + {(\frac{1}{3})}^{101} - \frac{1}{3} - {(\frac{1}{3})}^{3} - {(\frac{1}{3})}^{5} - . . . - {(\frac{1}{3})}^{99} \frac{- 8}{9} S = {(\frac{1}{3})}^{101} - \frac{1}{3} \frac{8}{9} S = \frac{1}{3} - \frac{1}{3^{101}} S = (\frac{1}{3} - \frac{1}{3^{101}}) \times \frac{9}{8} S = \frac{3}{8} - \frac{1}{8 \times 3^{99}}$

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Answer 2

a)

$S = 2 + 2^{3} + 2^{5} + . . . + 2^{51} \Rightarrow 4 S = 2^{3} + 2^{5} + 2^{7} + . . . + 2^{53} \Rightarrow 4 S - S = 2^{3} + 2^{5} + 2^{7} + . . . + 2^{53} - 2 - 2^{3} - 2^{5} - . . . - 2^{51} \Leftrightarrow 3 S = 2^{53} - 2 \Leftrightarrow S = \frac{2^{53} - 2}{3} b, S = \frac{1}{3} + {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + . . . + {(\frac{1}{3})}^{99} \frac{1}{9} S = {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + {(\frac{1}{3})}^{7} + . . . + {(\frac{1}{3})}^{101} \frac{1}{9} S - S = {(\frac{1}{3})}^{3} + {(\frac{1}{3})}^{5} + {(\frac{1}{3})}^{7} + . . . + {(\frac{1}{3})}^{101} - \frac{1}{3} - {(\frac{1}{3})}^{3} - {(\frac{1}{3})}^{5} - . . . - {(\frac{1}{3})}^{99} \frac{- 8}{9} S = {(\frac{1}{3})}^{101} - \frac{1}{3} \frac{8}{9} S = \frac{1}{3} - \frac{1}{3^{101}} S = (\frac{1}{3} - \frac{1}{3^{101}}) \times \frac{9}{8} S = \frac{3}{8} - \frac{1}{8 \times 3^{99}}$

Answer 3

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