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1. \(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{40.43}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{40}-\frac{1}{43}\)
\(=1-\frac{1}{43}\)
\(=\frac{42}{43}\)
2. Đặt \(A=\frac{2}{2}+\frac{2}{6}+\frac{2}{12}+...+\frac{2}{90}\)
\(=2.\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{9.10}\right)\)
\(=2.\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{9}-\frac{1}{10}\right)\)
\(=2.\left(1-\frac{1}{10}\right)\)
\(=2.\frac{9}{10}\)
\(=\frac{9}{5}\)
Ủng hộ mk nha !!! ^_^
1) 3/1×4 + 3/4×7 + 3/7×10 + ... + 3/40×43
= 1 - 1/4 + 1/4 - 1/7 + 1/7 - 1/10 + ... + 1/40 - 1/43
= 1 - 1/43
= 42/43
2) 2/2 + 2/6 + 2/12 + ... + 2/90
= 2 × (1/2 + 1/6 + 1/12 + ... + 1/90)
= 2 × (1/1×2 + 1/2×3 + 1/3×4 + ... + 1/9×10)
= 2 × (1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/9 - 1/10)
= 2 × (1 - 1/10)
= 2 × 9/10
= 9/5
a) 234 x 95 + 234 x 4 + 234 = 234 x ( 95 + 4 + 1 ) = 234 x 100 = 23400
a).234 x 95 + 234 x 4 + 234
= 234 x ( 95 + 4 + 1 )
= 234 x 100
= 23400
b) ( 1+1/2) x ( 1+1/3) x ( 1+1/4 )
= ( 2/2+1/2 ) x ( 3/3+1/3 ) x ( 4/4 + 1/4)
=3/2 + 4/3 + 5/4
= 18/12 + 16/12 + 20/12
= 54/12
= 9 /2
1\(\frac{5}{7}\)X \(\frac{3}{4}\)= \(\frac{9}{7}\)
\(\frac{10}{11}\): 1\(\frac{1}{3}\)= \(\frac{15}{22}\)
Ta đặt :1 = 5/7 x 3/4 = 9/7
=> : 10/11 : 1 X 1/3 = ?
<+> : 15/22 .
cHẮC CHẮN 100%%%
1/3xD=1/(2x4)+1/(4x6)+...+1/(98x100)
2/3xD=2/(2x4)+2/(4x6)+...+1/(98x100)
2/3xD= 1/2-1/4+1/4-1/6+...+1/98-1/100
2/3xD=1/2-1/100
2/3xD=49/100
D=147/200
\(1\frac{1}{3}\)x \(1\frac{1}{8}\)x \(1\frac{1}{15}\)x .......x \(1\frac{1}{99}\)= \(\frac{4}{3}\)x \(\frac{9}{8}\)x\(\frac{16}{15}\)x..........x \(\frac{100}{99}\)
=\(\frac{2.2}{1.3}\)x\(\frac{3.3}{2.4}\)x\(\frac{4.4}{3.5}\)x.......x \(\frac{10.10}{9.11}\)= \(\frac{2.3.4....10}{1.2.3.....9}\)x \(\frac{2.3.4....10}{3.4.5....11}\)
= \(\frac{10}{1}\)x\(\frac{2}{11}\)=\(\frac{20}{11}\)
4/3 x 9/8 x16/15 x ..... x 100/99
=2x2/1x3 x 3x3/2x4 x 4x4/3x5 x ... x 10x10/9x11
=2x3x4x....x10/1x2x3x..x9 x 2x3x4x...x10/3x4x5x...x11
=10 x 2/11=20/11
Đặt biểu thức trên là A ta có:
A = \(\frac{1}{3}\)+ \(\frac{1}{6}\)+ \(\frac{1}{12}\)+ \(\frac{1}{24}\)+ \(\frac{1}{48}\)+ \(\frac{1}{96}\)
A x 3 = \(1\)+ \(\frac{1}{2}\)+ \(\frac{1}{4}\)+ \(\frac{1}{8}\)+ \(\frac{1}{16}\)+ \(\frac{1}{32}\)
A x 3 = \(1\)+ \(1\)- \(\frac{1}{2}\)+ \(\frac{1}{2}\)- \(\frac{1}{4}\)+ \(\frac{1}{4}\)- \(\frac{1}{8}\)+ \(\frac{1}{8}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{32}\)
A x 3 = 2 - \(\frac{1}{32}\)= \(\frac{63}{32}\)
A = \(\frac{63}{32}\): 3 = \(\frac{63}{96}\)
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nhầm nhé
37,82 (6)