Tính
a, 2.4+4.6+6.8+......+100.102
b, 8.10+10.12+12.14+.....+98.100
c, 1.2.3+2.3.4+4.5.6+5.6.7
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FT
12 tháng 11 2017
\(B=2.4+4.6+6.8+...+98.100\)
\(B=2.\left(1.2\right)+2.\left(2.3\right)+2.\left(3.4\right)+...+2.\left(49.50\right)\)
\(B=2\left(1.2+2.3+3.4+....+49.50\right)\)
Đặt:
\(A=1.2+2.3+3.4+...+49.50\)
\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)
\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)
\(3A=49.50.51\)
\(A=\dfrac{49.50.51}{3}=41650\)
\(B=2A=41650.2=83300\)
NN
11 tháng 11 2017
A=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2)
A=1.2.4+2.3.4+...+50.51.4
A=4(1.2+2.3+...+50.51)
M= 1.2+2.3+...+50.51
3M=1.2.3+2.3.(4-1)+...+50.51.(52-49)
=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51
= 50.51.52
=132600
=> M=44200
=> A=4M=176800
RA
1
8 tháng 10 2019
A = 1×3+3×5+5×7+...+ 97×99+99×101
6A= 1×3×6+3×5×6+5×7×6+...+97×99×6+99×101×6
6A= 1×3×(5+1)+3×5×(7-1)+5×7×(9-3)+...+97×99×(101-95)+99×101×(103-97)
6A = 1×3×5-1×3+3×5×7-1×3×5+5×7×9-3×5×7+7×9×11-5×7×9+,,,+97×99×101-95×97×99+99×101×103-97×99×101
6A= 1×3+99×101×103
6A= 1029900
A= 171650
12 tháng 4 2023
b: 6B=2*4*6+4*6*6+6*8*6+...+46*48*6+48*50*6
=2*4*6-2*4*6+4*6*8-4*6*8+...-44*46*48+46*48*50-46*48*50+48*50*52
=48*50*52
=>B=20800
d: 9D=1*4*9+4*7*9+...+46*49*9
=1*4*2+1*4*7-1*4*7+1*7*10-1*7*10+...+46*49*52-46*49*43
=1*2*4+46*49*52
=117216
=>D=13024
a: 
VM
1
PT
4 tháng 4 2017
\(A = 1.4 + 2.5 + 3.6 + ...+ 99.102\)
\(A=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2\)
\(A=(1.2+2.3+3.4+...+99.100)+2.(1+2+3+...+99)\)
\(A=333300+9900\)
\(A=343200\)
\(B = 2.4 + 4.6 + 6.8 + ....+ 98.100 + 100.102\)
\(B=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2) \)
\(B=4(1.2+2.3+...+50.51) \)
\(M= 1.2+2.3+...+50.51 \)
\(3M=1.2.3+2.3.(4-1)+...+50.51.(52-49) \)
\(=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51 \)
\(= 50.51.52\)
\(=132600 \)
\(\Rightarrow\)\(M=44200 \)
\(\Rightarrow\) \(B=4M=176800\)
NK
1
CT
2
13 tháng 8 2015
\(\frac{3}{4.6}+\frac{3}{6.8}+\frac{3}{8.10}+\frac{3}{10.12}+\frac{3}{12.14}\)
=\(3.\left(\frac{1}{4.6}+\frac{1}{6.8}+\frac{1}{8.10}+\frac{1}{10.12}+\frac{1}{12.14}\right)\)
=\(\frac{3}{2}.\left(\frac{2}{4.6}+\frac{2}{6.8}+\frac{2}{8.10}+\frac{2}{10.12}+\frac{2}{12.14}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+\frac{1}{8}-\frac{1}{10}+\frac{1}{10}-\frac{1}{12}+\frac{1}{12}-\frac{1}{14}\right)\)
=\(\frac{3}{2}.\left(\frac{1}{4}-\frac{1}{14}\right)\)
=\(\frac{3}{2}.\left(\frac{7}{28}-\frac{2}{28}\right)\)
=\(\frac{3}{2}.\frac{5}{28}=\frac{15}{56}\)
4 tháng 5 2020
\(\sqrt[]{\frac{ }{ }\frac{ }{ }\hept{\begin{cases}\\\end{cases}}\hept{\begin{cases}\\\\\end{cases}}\orbr{\begin{cases}\\\end{cases}}^2}\)
Đặt A = 8.10 + 10.12 + 12.14 + ....... + 98.100
=> 6A = 8.10.12 - 8.10.12 + 10.12.14 - 10.12.14 + ...... + 98.100.102
=> 6A = 98.100.102
=> A = 98.100.102/6
=> A = 166600
c.1.2.3+2.3.4+4.5.6+5.6.7=6+24+120+210
=30+120+210
=150+210
=360