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B1 Nhân biểu tthức trên với 1/2 được
1/6+1/12/+1/20+....+1/110=1/2×3+1/3×4+.....+1/10×11
=1/2-1/3+1/3-1/4+.....+1/10-1/11=1/2-1/11=9/22
B2
B.1/1×2+1/2×3+.....+1/99×100=1-1/2 +1/2-1/3+....+1/99-1/100=1-1/100=99/100
Phần a sai đề phải llà1/2×4+1/4×6+.....+1/8×10 mới làm đc nhé
ta có :13/15=13.111/15.111=1433/1665
có :1-1443/1665=222/1665;1-1333/1555=222/1555
mà:222/1665<222/1555=>1-1443/1665<1-1333/1555
=>1443/1665>1333/1555
=>13/15>1333/1555
\(\frac{1333}{1555}\)= \(\frac{13}{15}\)nên \(\frac{13}{15}\)=\(\frac{1333}{1555}\)
a) \(\frac{14}{15}+\frac{3}{11}+\frac{1}{15}+\frac{3}{11}+\frac{10}{22}\)
\(=\left(\frac{14}{15}+\frac{1}{15}\right)+\left(\frac{3}{11}+\frac{3}{11}\right)+\frac{10}{22}\)
\(=1+1+\frac{10}{22}\)
\(=2+\frac{10}{22}\)
\(=\frac{27}{11}\)
b) 9,25 + 9,25 x 8 + 9,25
= 9,25 x ( 8 + 1 + 1 )
= 9,25 x 10
= 92,5
\(\frac{3}{5×3}+\frac{3}{5×7}+\frac{3}{7×9}+\frac{3}{9×11}+\frac{3}{11×13}\)
\(=\frac{3}{2}×\left(\frac{2}{3×5}+\frac{2}{5×7}+\frac{2}{7×9}+\frac{2}{9×11}+\frac{2}{11×13}\right)\)
\(=\frac{3}{2}×\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{3}{2}×\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{3}{2}×\left(\frac{13}{39}-\frac{3}{39}\right)\)
\(=\frac{3}{2}×\frac{10}{39}\)
\(=\frac{5}{13}\)
\(\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+\frac{3}{9.11}+\frac{3}{11.13}\)
\(=\frac{3}{2}\left(\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{ 1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11} +\frac{1}{11}-\frac{1}{13}\right)\)
\(=\frac{3}{2}.\left(\frac{1}{3}-\frac{1}{13}\right)\)
\(=\frac{3}{2}.\frac{10}{39}\)
\(=\frac{15}{39}\)
27/8 - 7/3 + 4/3 - 2
= 27/8 - (7/3 - 4/3) - 2
= 27/8 - 1 - 2
=27/8 - 3
= 3/8
\(=\left(15\frac{2}{3}+12\frac{1}{3}\right):3-\frac{8}{3}\)
\(=28:3-\frac{8}{3}\)
\(=\frac{28}{3}-\frac{8}{3}\)
\(=\frac{20}{3}\)
\(15\frac{2}{3}:3+12\frac{1}{3}:3-\frac{8}{3}\)
\(=\left(15\frac{2}{3}+12\frac{1}{3}\right):3-\frac{8}{3}\)
\(=28:3-\frac{8}{3}\)
\(\frac{28}{3}-\frac{8}{3}\)
\(\frac{20}{3}\)