Tính hợp lí nếu có thể
a.(1 + 3 + 5 + ……. + 2007 + 2009 + 2011)(125125.127 – 127127.125)
b.1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143 + 1/195
Tính hợp lí nếu có thể
a.(1 + 3 + 5 + ……. + 2007 + 2009 + 2011)(125125.127 – 127127.125)
b.1/3 + 1/15 + 1/35 + 1/63 + 1/99 + 1/143 + 1/195
$a.(1 + 3 + 5 + ……. + 2007 + 2009 + 2011)(125125.127 – 127127.125)$
$= (1 + 3 + 5 + ……. + 2007 + 2009 + 2011)(125.1001.127-127.1001.125)$
$= (1 + 3 + 5 + ……. + 2007 + 2009 + 2011).0$
$=0$
$b$) `1/3 + 1/{15} + 1/{35} + 1/{63} + 1/{99} + 1/{143} + 1/{195}`
`= 1/{1.3} + 1/{3.5} + 1/{5.7} + 1/{7.9} + 1/{9.11} + 1/{11.13} + 1/{13.15}`
`= 1/2 . (2/{1.3} + 2/{3.5} + 2/{5.7} + 2/{7.9} + 2/{9.11} + 2/{11.13} + 2/{13.15})`
`= 1/2 . (1 – 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/{11} + 1/{11} – 1/{13} + 1/{13} – 1/{15})`
`= 1/2 .( 1 – 1/{15})`
`= 1/2 . {14}/{15}`
`= 7/{15}`
Giải thích các bước giải:
Bạn tham khảo:
a) $(1+3+5+…+2007+2009+2011)(125125.127-127127.125)$
$=(1+3+5+…+2007+2009+2011)(125.1001.127-127127.125)$
$=(1+3+5+…+2007+2009+2011)(125.127127-127127.125)$
$=(1+3+5+…+2007+2009+2011).0$
$=0$
b) $\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}+\frac{1}{195}$
$=\frac{1}{1}.\frac{1}{3}+\frac{1}{3}.\frac{1}{5}+\frac{1}{5}.\frac{1}{7}+\frac{1}{7}.\frac{1}{9}+\frac{1}{9}.\frac{1}{11}+\frac{1}{11}.\frac{1}{13}+\frac{1}{13}.\frac{1}{15}$
$=\frac{1}{2}(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+\frac{2}{9.11}+\frac{2}{11.13}+\frac{2}{13.15})$
$=\frac{1}{2}(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15})$
$=\frac{1}{2}(1-\frac{1}{15})$
$=\frac{1}{2}.\frac{14}{15}$
$=\frac{14}{30}=\frac{7}{15}$