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DD
3
25 tháng 1 2016
Dat A=1.2.3+2.3.4+3.4.5+...+98.99.100
4A=1.2.3.4+2.3.4.4+3.4.5.4+...+98.99.100.4
4A=1.2.3.4+2.3.4.(5-1)+3.4.5.(6-2)+...+98.99.100.(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100
4A=98.99.100.101
A=\(\frac{98.99.100.101}{4}\)
A=24497550
Ung ho minh nha
Tick minh thi may man ca nam do!!!!!
Tick minh nha Dinh Duc Hung
DN
1 tháng 11 2023
Coi A = 1.2.3 + 2.3.4 +... + 98.99.100
4A = 1.2.3.4 + 2.3.4.4 +... + 98.99.100.4
4A = 1.2.3.4 + 2.3.4.(5-1) +... + 98.99.100.(101-97)
4A = 1.2.3.4+2.3.4.5-1.2.3.4 + ... + 98.99.100.101-97.98.99.100
4A = 98.99.100.101
4A =97990200
A = 97990200: 4
A=24497550
30 tháng 9 2015
mình làm cách cấp 2
A = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ........ + 98.99.(100 - 97)
A = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ........ + 98.99.100 - 97.98.99
A = (1.2.3 + 2.3.4 + 3.4.5 + ....... + 98.99.100) - (1.2.3 + 2.3.4 + ..... + 97.98.99)
A = 98.99.100
30 tháng 9 2015
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4
4 tháng 5 2015
Ta có :
\(4B=1\times2\times3\times\left(4-0\right)+2\times3\times4\times\left(5-1\right)+3\times4\times5\times\left(6-2\right)+...+98\times99\times100\times\left(101-97\right)\)\(=\left(1\times2\times3\times4+2\times3\times4\times5+.....+98\times99\times100\times101\right)\)\(-\left(0\times1\times2\times3+1\times2\times3\times4+.....+97\times98\times99\times100\right)\)
\(\Rightarrow\frac{98\times99\times100\times101}{4}=24497550\)
28 tháng 8 2016
Đặt S=1.2.3+2.3.4+...+98.99.100
=>4S=1.2.3.4+2.3.4.4+...+98.99.100.4
=>3S=1.2.3(4-0)+2.3.4(5-1)+....+98.99.100(101-97)
=>4S=1.2.3.4-0.1.2.3+2.3.4.5-1.2.3.4+....+98.99.100.101-97.98.99.100
=>4S=98.99.100.101
=>S=24497550
NN
Nguyễn Ngọc Anh Minh
CTVHS
VIP
20 tháng 7 2023
a/
\(b=\dfrac{1}{1.3}+\dfrac{1}{3.5}+\dfrac{1}{5.7}+...+\dfrac{1}{97.99}\)
\(2b=\dfrac{3-1}{1.3}+\dfrac{5-3}{3.5}+\dfrac{7-5}{5.7}+...+\dfrac{99-97}{97.99}=\)
\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{97}-\dfrac{1}{99}=\)
\(=1-\dfrac{1}{99}=\dfrac{98}{99}\Rightarrow b=\dfrac{98}{2.99}=\dfrac{49}{99}\)
b/
\(c=\dfrac{3-1}{1.2.3}+\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{100-98}{98.99.100}=\)
\(=\dfrac{1}{1.2}-\dfrac{1}{2.3}+\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+\dfrac{1}{98.99}-\dfrac{1}{99.100}=\)
\(=\dfrac{1}{2}-\dfrac{1}{99.100}\)
c/
\(\dfrac{2}{5}.d=\dfrac{4-2}{2.3.4}+\dfrac{5-3}{3.4.5}+...+\dfrac{100-98}{98.99.100}+\dfrac{101-99}{99.100.101}=\)
\(=\dfrac{1}{2.3}-\dfrac{1}{3.4}+\dfrac{1}{3.4}-\dfrac{1}{4.5}+...+\dfrac{1}{98.99}-\dfrac{1}{99.100}+\dfrac{1}{99.100}-\dfrac{1}{100.101}=\)
\(=\dfrac{1}{2.3}-\dfrac{1}{100.101}\Rightarrow d=\left(\dfrac{1}{2.3}-\dfrac{1}{100.101}\right):\dfrac{2}{5}\)
7 tháng 2 2016
Đặt A=1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100
4A=(1.2.3+2.3.4+3.4.5+4.5.6+...+98.99.100)4
4A=1.2.3(4-0)+2.3.4(5-1)+3.4.5(6-2)+4.5.6(7-3)+...+98.99.100(101-97)
4A=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+4.5.6.7-3.4.5.6+...+98.99.100.101-97.98.99.100
4A=1.2.3.4-1.2.3.4+2.3.4.5-2.3.4.5+3.4.5.6-3.4.5.6+...+97.98.99.100-97.98.99.100+98.99.100.101
4A=98.99.100.101
=>A=98.99.100.101/4
Đặt S = 1.2.3 + 2.3.4 + 3.4.5 + .... + 98.99.100
=> 4S = 1.2.3.4 + 2.3.4.4 + 3.4.5.4 + ... + 98.99.100.4
=> 4S = 1.2.3.4 + 2.3.4.( 5 - 1 ) + 3.4.5.( 6 - 2 ) + .... + 98.99.100.( 101 - 97 )
=> 4S = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + 3.4.5.6 - 2.3.4.5 + .... + 98.99.100.101 - 97.98.99.100
=> 4S = ( 1.2.3.4 - 1.2.3.4 ) + ( 2.3.4.5 - 2.3.4.5 ) + ...... + ( 97.98.99.100 - 97.98.99.100 ) + 98.99.100.101
=> 4S = 98.99.100.101
=> S = \(\frac{98.99.100.101}{4}\)
=> S = 24497550
99.100.101:3