Tính a,1/2 – 1/4 + 1/13 + 1/8 b, 3/2 + 5/4 + 9/8 + 17/16 + 33/32 + 65/64 – 7

Đáp án:

 $a) \dfrac{47}{104}\\
b) \dfrac{-1}{64}$

Giải thích các bước giải:

 $a) \dfrac{1}{2}-\dfrac{1}{4}+\dfrac{1}{13}+\dfrac{1}{8}\\
=\dfrac{4}{8}-\dfrac{2}{8}+\dfrac{1}{8}+\dfrac{1}{13}\\
=\dfrac{3}{8}+\dfrac{1}{13}\\
=\dfrac{39}{104}+\dfrac{8}{104}\\
=\dfrac{47}{104}\\
b) \dfrac{3}{2}+\dfrac{5}{4}+\dfrac{9}{8}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{6}{4}+\dfrac{5}{4}+\dfrac{9}{8}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{11}{4}+\dfrac{9}{8}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{22}{8}+\dfrac{9}{8}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{31}{8}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{62}{16}+\dfrac{17}{16}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{158}{32}+\dfrac{33}{32}+\dfrac{65}{64}-7\\
=\dfrac{191}{32}+\dfrac{65}{64}-7\\
=\dfrac{382}{64}\dfrac{65}{64}-7\\
=\dfrac{447}{64}-7\\
=\dfrac{447}{64}-\dfrac{448}{64}\\
=\dfrac{-1}{64}$