Question

S= 1.2 + 2.3 + 3.4 + ..... + 99.100

Answer 1

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

Answer 2

=> 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

Answer 3

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 

Answer 4

\(S=1.2+2.3+3.4+......+99.100\)

\(\frac{1}{S}=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{99.100}\)

\(\frac{1}{S}=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+.....+\frac{1}{99}-\frac{1}{100}\)

\(\frac{1}{S}=\frac{1}{1}-\frac{1}{100}\)

\(\frac{1}{S}=\frac{99}{100}\)

\(S=1:\frac{99}{100}=\frac{1.100}{99}=\frac{100}{99}\)

Answer 5

4513.5

Answer 6

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

Answer 7

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 .....

Answer 8

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

;

Answer 9

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