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\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
làm giống như trên
\(c,=\frac{1}{8}.\left(\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{3-1}{1.2.3}+\frac{4-2}{2.3.4}+\frac{5-3}{3.4.5}+...+\frac{50-48}{48.49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+\frac{1}{3.4}-\frac{1}{4.5}+...+\frac{1}{48.49}-\frac{1}{49.50}\right)\)
\(=\frac{1}{16}.\left(\frac{1}{2}-\frac{1}{2450}\right)=\frac{1}{16}.\left(\frac{1225}{2450}-\frac{1}{2450}\right)=\frac{153}{4900}\)
\(d,=\frac{5}{7}.\left(\frac{7}{1.5.8}+\frac{7}{5.8.12}+\frac{7}{8.12.15}+...+\frac{7}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{8-1}{1.5.8}+\frac{12-5}{5.8.12}+\frac{15-8}{8.12.15}+...+\frac{40-33}{33.36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{1.5}-\frac{1}{5.8}+\frac{1}{5.8}-\frac{1}{8.12}+\frac{1}{8.12}-\frac{1}{12.15}+...+\frac{1}{33.36}-\frac{1}{36.40}\right)\)
\(=\frac{5}{7}.\left(\frac{1}{5}-\frac{1}{1440}\right)=\frac{5}{7}.\left(\frac{288}{1440}-\frac{1}{1440}\right)=\frac{41}{288}\)
P/S: . là nhân nha
- số số hạng của tổng là:
(15-1):2+1=8(số hạng)
Tổng trên có giá trị là:
(15+1).8:2=64
-số số hạng của tổng là:
(16-2):2+1=8(số hạng)
Tổng trên có giá trị là:
(16+2).8:2=72
-số số hạng của tổng là:
(22-1):3+1=8(số hạng)
Tổng trên có giá trị là:
(22+1).8:2=92
1+3+5+7+9+11+13+15=(1+15)+(3+13)+(5+11)+(7+9)=16x4=64
1+5+9+13+17+21+25+29+33+37=(1+37)+(5+33)+(9+29)+(13+25)+(17+21)=38x5=190
a , Theo thứ tự từ bé đến lớn : 1/12 , 2/3 , 3/4 , 5/6
b, Tính
a, 3/ 4 + 2/3 + 5/12 = 9/12 + 8/12 + 5/12 = 11/6
b, 7/8 - 7/16 - 11/32 = 28/32 - 14/32 - 11/32 = 3/32
c, 3/5 x 2/7 x 5/6 = 3 x 2 x 5 / 5 x 7 x 6 = 3 x 2 x 5 / 5 x 7 x 3 x 2 = 1/7
d , 15/16 : 3/8 x 3/4 = 15/16 x 8/3 x 3/4 = 15 x 8 x 3 / 16 x 3 x4 = 3 x 5 x 8 x 3 / 8 x 2 x 3 x 4 = 15/8
a) 1/12; 2/3; 3/4; 5/6
b)
a) 3/4 + 2/3 + 5/12 = 9/12 + 8/12 + 5/12 = 17/12 + 5/12 = 22/12 = 11/6
b) 7/8 - 7/16 - 11/32 = 28/32 - 14/32 - 11/32 = 14/32 - 11/32 = 3/32
c) 3/5 x 2/7 x 5/6 = 6/35 x 5/6 = 30/210 = 1/70
d) 15/16 : 3/8 x 3/4 = 15/16 x 8/3 x3/4 = 120/48 x 3/4 = 360/192 = 8/15
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
(6-14/5)×25/8-18/5×1/4
=16/5 * 25/8 - 18/5 * 1/4
=10 - 9/10
=91/10
4 và 2/5-1 và 3/7-1 và 4/7
=22/5 - 10/7 - 11/7
=104/35 - 11/7
=7/5
8/11×(7/4-3/8)
=8/11 * 11/8
=1
8/5×(3/7+1/4)
=8/5 * 3/28
=6/35
A = (29 x 2019 + 71 x 2019) : 100 - 19
A = [2019 x (29 + 71)] : 100 - 19
A = (2019 x 100) : 100 - 19
A = 2019 - 19
A = 2000
B = (3/4 + 5/6) : 1\(\frac{7}{12}\)- 1/2
B = (9/12 + 10/12) : 19/12 - 1/2
B = 19/12 : 19/12 - 1/2
B = 1 - 1/2
B = 1/2
A = (29 x 2019 + 71 x 2019) : 100 - 19
A = [2019 x (29 + 71)] : 100 - 19
A = (2019 x 100) : 100 - 19
A = 2019 - 19
A = 2000
a, QUY ĐỒNG PHÂN SỐ :
MSC=280
\(\frac{2}{5}\)\(=\)\(\frac{112}{280}\)
\(\frac{4}{7}\)\(=\)\(\frac{160}{280}\)
\(\frac{5}{8}\)\(=\)\(\frac{175}{280}\)
mà \(\frac{112}{280}\)\(< \)\(\frac{160}{280}\)\(< \)\(\frac{175}{280}\)\(=>\)\(\frac{2}{5}\)\(< \)\(\frac{4}{7}\)\(< \)\(\frac{5}{8}\)
k cho anh nha anh mỏi tay quá lên chỉ làm dc câu a tý làm câu b sau