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\(\frac{6}{1\times3\times7}+\frac{6}{3\times7\times9}+\frac{6}{7\times9\times13}+\frac{6}{9\times13\times15}+\frac{6}{13\times15\times9}\)
\(=\frac{1}{1\times3}-\frac{1}{3\times7}+\frac{1}{3\times7}-\frac{1}{7\times9}+\frac{1}{7\times9}-\frac{1}{9\times13}+\frac{1}{9\times13}-\frac{1}{13\times15}+\frac{1}{13\times15}-\frac{1}{15\times9}\)
\(=\frac{1}{1\times3}-\frac{1}{15\times9}=\frac{1}{3}-\frac{1}{135}=\frac{45}{135}-\frac{1}{135}=\frac{44}{135}\)
= 54/6. [6/1.3.7 +6/3.7.9 +6/7.9.13 + 6/9.13.15]
=54/6 [1/1.3-1/3.7 + 1/3.7 - 1/7.9 + 1/7.9 - 1/9.13 + 1/9.13 -1/13.15]
=54/6[1/3- 1/13.15]
=54/6 .64/195
=192/65
Thời gian xe máy đi trước ô tô:
8 giờ 6 phút - 6 giờ 30 phút = 1 giờ 36 phút = 1,6 giờ
Xe máy đi trước ô tô:
45 x 1,6 = 72(km)
Hiệu 2 vận tốc:
54 - 45 = 9(km/h)
Từ lúc ô tô xuất phát tới lúc đuổi kịp xe máy mất:
72:9=8(giờ)
Ô tô đuổi kịp xe máy lúc:
8 giờ 6 phút + 8 giờ = 16 giờ 6 phút
\(\dfrac{2}{3}+\dfrac{2}{6}+\dfrac{2}{12}+\dfrac{2}{24}+\dfrac{2}{48}+\dfrac{2}{96}+\dfrac{2}{192}\\ =\dfrac{128}{192}+\dfrac{64}{192}+\dfrac{32}{192}+\dfrac{16}{192}+\dfrac{8}{192}+\dfrac{4}{192}+\dfrac{2}{192}\\ =\dfrac{128+64+32+16+8+4+2}{192}\\ =\dfrac{254}{192}=\dfrac{127}{96}\)
1.3.77−1+3.7.99−3+7.9.1313−7+9.13.1515−9+\frac{19-13}{13.15.19}+13.15.1919−13
=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}=1.31−3.71+3.71−7.91+7.91−9.131+9.131−13.151+13.151−15.191
=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}=1.31−15.191=28595−2851=28594
b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)b,=61.(1.3.76+3.7.96+7.9.136+9.13.156+13.15.196)
làm giống như trên
c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)c,=81.(1.2.31+2.3.41+3.4.51+...+48.49.501)
=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)=161.(1.2.32+2.3.42+3.4.52+...+48.49.502)
=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)=161.(1.2.33−1+2.3.44−2+3.4.55−3+...+48.49.5050−48)
=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)=161.(1.21−2.31+2.31−3.41+3.41−4.51+...+48.491−49.501)
=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}=161.(21−24501)=161.(24501225−24501)=4900153
d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)d,=75.(1.5.87+5.8.127+8.12.157+...+33.36.407)
=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)=75.(1.5.88−1+5.8.1212−5+8.12.1515−8+...+33.36.4040−33)
=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)=75.(1.51−5.81+5.81−8.121+8.121−12.151+...+33.361−36.401)
=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}=75.(51−14401)=75.(1440288−14401)=28841
P/S: . là nhân nha
(x+1/10).5/6=3-7/6
(x+1/10).5/6=18/6-7/6
(x+1/10).5/6=11/6
x+1/10=11/6:5/6
x+1/10=11/6.6/5
x+1/10=11/5
x =11/5-1/10
x=22/10-1/10
x=21/10
dấu . là dấu nhân nha
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