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1+2+3+4+5+6+7+8+9+10+11+12+13+14
=(1+14)+(2+13)+(3+12)+(4+11)+(5+10)+(6+9)+(7+8)
= 15+15+15+15+15+15+15
=105
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
\(a,=\frac{7-1}{1.3.7}+\frac{9-3}{3.7.9}+\frac{13-7}{7.9.13}+\frac{15-9}{9.13.15}\)\(+\frac{19-13}{13.15.19}\)
\(=\frac{1}{1.3}-\frac{1}{3.7}+\frac{1}{3.7}-\frac{1}{7.9}+\frac{1}{7.9}-\frac{1}{9.13}+\frac{1}{9.13}-\frac{1}{13.15}+\frac{1}{13.15}-\frac{1}{15.19}\)
\(=\frac{1}{1.3}-\frac{1}{15.19}=\frac{95}{285}-\frac{1}{285}=\frac{94}{285}\)
\(b,=\frac{1}{6}.\left(\frac{6}{1.3.7}+\frac{6}{3.7.9}+\frac{6}{7.9.13}+\frac{6}{9.13.15}+\frac{6}{13.15.19}\right)\)
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
1+2-3-4+5+6-7-8+9+10-11-12+13+14....................+301+302
=1+(2-3-4+5)+(6-7-8+9)+(10-11-12+13)+...................+(298-299-300+301)+302
=1+302
=303
1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + 13 + 14 + ... + 301 + 302
= (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) + (9 + 10 - 11 - 12) + ... + (297 + 298 - 299 - 300) + 301 + 302
= -4 - 4 - 4 - ... - 4 + 301 + 302
= -(4 + 4 + ... + 4) + 603
= -300 + 603 = 303
Trả lời:
a, \(A=5\times\left(\frac{1}{5}+\frac{1}{7}\right)-\left(\frac{2}{5}+\frac{2}{17}+\frac{6}{10}+\frac{9}{51}\right)\)
\(A=5\times\left(\frac{1}{5}+\frac{1}{7}\right)-\left(\frac{2}{5}+\frac{2}{17}+\frac{3}{5}+\frac{3}{17}\right)\)
\(A=5\times\left(\frac{1}{5}+\frac{1}{7}\right)-\left(\frac{5}{5}+\frac{5}{17}\right)\)
\(A=5\times\left(\frac{1}{5}+\frac{1}{7}\right)-5\times\left(\frac{1}{5}+\frac{1}{17}\right)\)
\(A=5\times\left(\frac{1}{5}+\frac{1}{7}-\frac{1}{5}-\frac{1}{7}\right)\)
\(A=5\times\left(\frac{1}{7}-\frac{1}{17}\right)\)
\(A=5\times\frac{10}{119}\)
\(A=\frac{50}{119}\)
b, \(B=\frac{2003\times14+1988+2001\times2002}{2002+2002\times503+504\times2002}\)
\(B=\frac{\left(2002+1\right)\times14+1988+2001\times2002}{2002\times\left(1+503+504\right)}\)
\(B=\frac{2002\times14+14+1988+2001\times2002}{2002\times1008}\)
\(B=\frac{2002\times14+2002+2001\times2002}{2002\times1008}\)
\(B=\frac{2002\times\left(14+1+2001\right)}{2002\times1008}\)
\(B=\frac{2002\times2016}{2002\times1008}\)
\(B=2\)
c, Sửa dề
\(\left(4,58\div3,27+5,23\div3,27\right)\times4,08-4,08\)
\(=\left[\left(4,58+5,23\right)\div3,27\right]\times4,08-4,08\)
\(=\left(9,81\div3,27\right)\times4,08-4,08\)
\(=3\times4,08-4,08\)
\(=4,08\times\left(3-1\right)\)
\(=4,08\times2\)
\(=8,16\)
d, \(\frac{6}{11}+\frac{7}{17}+\frac{8}{25}+\frac{10}{17}+\frac{16}{11}+\frac{17}{25}\)
\(=\left(\frac{6}{11}+\frac{16}{11}\right)+\left(\frac{7}{17}+\frac{10}{17}\right)+\left(\frac{8}{25}+\frac{17}{25}\right)\)
\(=2+1+1\)
\(=4\)
a) 11/15 + 5/7 + 2/7 + 4/15
= ( 11/15 + 4/15 ) + ( 5/7 + 2/7 )
= 1 + 1
= 2
b ) 5/9 x 1/2 + 5/9 x 6/4
= 5/9x ( 1/2 + 6/4 )
= 5/9 x 2
= 10/9
c) 7/8 : 1/2 + 9/8 : 1/2
= ( 7/8 + 9/8 ) ; 1/2
= 2 : 1/2
= 4
d) 17/10 + 1/2 - 7/10
= ( 17/10 - 7/10 ) + 1/2
= 1 + 1/2
= 3/2
- 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