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Ta có:
(1/2 + 1/4 + 1/8 + 1/16) = 8/16 + 4/16 + 2/16 + 1/16 = 15/16.
1/2 + 1/6 + 1/12 + 1/20 +…+ 1/132 = 1/(1.2) + 1/(2.3) + 1/(3.4) + 1/(4.5) +…+1/(11.12)
= (1 – 1/2) + (1/2 – 1/3) + (1/3 – 1/4) + (1/4 – 1/5) +…+ (1/11 – 1/12)
= 1 – 1/12 = 11/12
Vậy x = (15/16) : (11/12) = 45/44.
(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+1/20+...+1/132
(1-1/2+1/2-1/4+1/4-1/8+1/8-1/16):x=1/1x2+1/2x3+1/3x4+1/4x5+...+1/11x12
(1-1/16):x=1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+...+1/11-1/12
15/16:x=1-1/12
15/16:x=11/12
x=15/16:11/12
x=45/44
(1/2+1/4+1/8+1/16):x=1/2+1/6+1/12+.....+1/132
15/16 : x = 1/1x2+1/2x3+1/3x4+.........+1/11x12
15/16 : x = 1-1/2+1/2-1/3+1/3-1/4+........+1/11-1/12
15/16 :x = 1-1/12
15/16 : x = 11/12
x = 15/16 : 11/12
x= 45/44
\(a)\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{132}\)
\(=\frac{22}{132}+\frac{11}{132}+\frac{1}{20}+\frac{1}{132}\)
\(=\frac{33}{132}+\frac{1}{20}+\frac{1}{132}\)
\(=\frac{34}{132}+\frac{1}{20}\)
\(=\frac{17}{66}+\frac{1}{20}\)
\(=\frac{203}{660}\)
\(a,\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{132}\)
\(=\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{132}\)
\(=\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}\right)+\frac{1}{132}\)
\(=\left(\frac{1}{2}-\frac{1}{5}\right)+\frac{1}{132}\)
\(=\frac{3}{10}+\frac{1}{132}\)
\(=\frac{198}{660}+\frac{5}{660}\)
\(=\frac{203}{660}\)
\(A=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\)\(\frac{1}{132}\)= \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+...+\frac{1}{11\cdot12}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{11}-\frac{1}{12}\)\(=1-\frac{1}{12}=\frac{11}{12}\)
1/2 + 1/6 + 1/20 +........+1/110 + 1/132 =
1/2 + 1/2x3 + 1/3x4 + 1/4x5 +....+ 1/10x11 + 1/11x12
= 1/2 + 1/2 - 1/3 + 1/3 -1/4 + 1/4 - 1/5 +...+ 1/10 - 1/11 +1/11 - 1/12
= 1/2 + 1/2 - 1/12 = 1 - 1/12 = 11/12
Đáp số : 11/12
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