Gọi A là biểu thức ta có:
A = 1.2+2.3+3.4+......+99.100
Gấp A lên 3 lần ta có:
A . 3 = 1.2.3 + 2.3.3 + 3.4.3 + … + 99.100.3
A . 3 = 1.2.3 + 2.3.(4 - 1) + 3.4.( 5 - 2) + … + 99.100. (101 - 98)
A . 3 = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + … + 99.100.101 - 98.99.100
A . 3 = 99.100.101
A = 99.100.101 : 3
A = 33.100.101
A = 333 300
=> 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101 => 3S = 3.33.100.101
=> S=33.100.101= 333300
S= 1.2 + 2.3 + 3.4 + ...+ 99.100
\Rightarrow 3S = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
3S= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
3S= 1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...-97.98.99+99.100.101-98.99.100
3S = 99.100.101 \Rightarrow 3S = 3.33.100.101
\Rightarrow S=33.100.101= 333300
\(S=1.2+2.3+3.4+......+99.100\)
\(\frac{1}{S}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)
\(\frac{1}{S}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)
\(\frac{1}{S}=\frac{1}{1}-\frac{1}{100}\)
\(\frac{1}{S}=\frac{99}{100}\)
\(S=1:\frac{99}{100}=\frac{1.100}{99}=\frac{100}{99}\)
3A=1.2.3+2.3.3+3.4.3+....+99.100.3
=1.2.3+2.3.(4-1)+3.4.(5-2)+....+99.100.(101-98)
=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+.....+99.100.101-98.99.100
=99.100.101
A=33.100.101=333300
S=1.2+2.3+3.4+...+99.100 S=1.100 S=100 (gạch hết các số 2, 3 ,4 ,5,6,7....99) làm chuẩn không cần chỉnh cô giáo tớ dạy thế . k nha .....
S=1*2+2*3+...+99*100
3S=1*2*3+2*3*(4-1)+...+99*100*(101-98)
3S=1*2*3+2*3*4-1*2*3+...+99*100*101-98*99*100
3S=99*100*101=999900
S=999900 : 3 = 333300
;
3S = 1.2.3 + 2.3.3 + 3.3.4 +...+ 3.99.100
Đặt M = 1.2.3 + 2.3.4 + 3.4.5 +...+ 99.100.101
=>M - 3S = 1.2.3 - 1.2.3 + 2.3.( 4 - 3 ) + 3.4.( 5 - 3 ) +...+ 99.100.( 101 - 3 )
= 1.2.3 + 2.3.4 + 3.4.5 +...+ 99.100.101
=> M - 3S = M - 99.100.101
=> S = 99.100.101/3
S = 333300