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A = 1/1 - 1/2 + 1/2 - ....-1/50 = 1-1/50 = 49/50
B = 1/2 . (1/3 - 1/7 + 1/7 -.....-1/27) = 1/2. (1/3 - 1/27)
B = 1/2. 8/27 = 4/27


Ax3=(1x2+2x3+3x4+...+49x50)x3
Ax3=1x2x3+2x3x3+3x4x3+...+49x50x3
Ax3=1x2x(3-0)+2x3x(4-1)+3x4x(5-2)+...+49x50x(51-48)
Ax3=1x2x3-0x1x2+2x3x4-1x2x3+3x4x5-2x3x4+...+49x50x51- 48x49x50
Ax3=49x50x51
A =(49x50x51):3
A =41650
Đúng thì tích cho mình nhé!

\(1+\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+...+\frac{1}{99\cdot100}+\frac{1}{100\cdot101}\)
\(=1+1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}+\frac{1}{100}-\frac{1}{101}\)
\(=1+1-\frac{1}{101}=2-\frac{1}{101}=1\frac{100}{101}=\frac{201}{101}\)
=1+1/1-1/2+1/2-1/3+1/3-1/+1/4-1/5+...+1/99-1/100+1/100-1/101
=1+1-1/101
=201/101
3S = 3 X4 X 3 + 4 X 5 X 3 +................+ 49 X 50 X 3
3S = 3 X 4 X ( 5 - 2 ) + 4 X 5 X ( 6 - 3 ) + .................. + 49 X 50 X ( 51 - 48 )
3S = 3 X 4 X 5 - 2 X 3 X 4 + 4 X 5 X 6 - 3 X 4 X 5 +............ + 49 X 50 X 51 - 48 X 49 X 50
3S = - ( 2 X 3 X 4 ) + ( 3 X 4 X 5 - 3 X 4 X 5 ) + ( 4 X 5 X 6 - 4 X 5 X 6 ) + ........... + ( 48 X 49 X 50 - 48 X 49 X 50 ) + 49 X 50 X 51
3S = - ( 2 X 3 X 4 ) + 0 + 0 + ...........+ 0 + 49 X 50 X 51
3S = - 24 + 124950
3S = 124926=> S = 124926 : 3 => S = 41642
Ta có : S = 3.4 + 4.5 + 5.6 +.....+49.50
=>3S = - 2.3.4 + 3.4.5 - 3.4.5 + ..... + 49.50.51
=> 3S = -24 + 49.50.51
=> 3S = -24 + 124950 = 124926
=> S = 124926/3 = 41642