Question

B=1.2+2.3+3.4+...+98.99+99.100

Answer 1

Ta có : B = 1.2 + 2.3 + 3.4 + ... + 99.100

=> 3B = 1.2.3 + 2.3.3 + 3.4.3 + ... + 99.100.3

=> 3B = 1.2.3 + 2.3.(4 - 1) + 3.4.(5 - 2) + ... + 99.100.(101 - 98)

=>3B = 1.2.3 + 2.3.4 - 1.2.3 + 3.4.5 - 2.3.4 + ... + 99.100.101 - 98.99.100

=> 3B = 99.100.101

=> 3B = 999900

=> B = 333300

Vậy B = 333300

Answer 2

           Bài làm :

Ta có :

B= 1.2 + 2.3 + 3.4 + ...+ 99.100

=>3B = 1.2.3+2.3.3+3.4.3+...+98.99.3+99.100.3
<=>3B= 1.2.3+2.3(4-1)+3.4(5-2)+...+98.99(100-97)+99.100(101-98)
<=>3B= 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 = 999900

<=> B = 999900 : 3 = 333300

Vậy B = 333300

Answer 3

Có: \(3a\left(a+1\right)=\left[\left(a+2\right)-\left(a-1\right)\right].a\left(a+1\right)\)

\(=a\left(a+1\right)\left(a+2\right)-\left(a-1\right)a\left(a+1\right)\)

Xét \(B=1.2+2.3+3.4+...+98.99+99.100\)

\(\Rightarrow3B=3.1.2+3.2.3+3.3.4+...+3.98.99+3.99.100\)

\(=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(=-0.1.2+99.100.101=99.100.101\)

\(\Rightarrow B=33.100.101\)