Question

A=1.2+2.3+...+99.100 

tính tổng

Answer 1

Tk:
Đặt P = 1.2+2.3+3.4+...+99.100

3P = 1.2.3+2.3.3+3.4.3+...+99.100+3

3P = 1.2 (3-0) +2.3(4-1)+3.4(5-2) +...+ 99.100( 101-98)

3P = ( 1.2.3 + 2.3.4 + 3.4.5 + 99.100.101 ) -( 0.1.2 + 1.2.3 + 2.3.4 + ....+ 98.99.100)

3P = 99.100.101 - 0.1.2

3P = 999900 - 0

3P = 999900

P = 999900 : 3

P = 333300

Answer 2

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

\(\Rightarrow3A=1.2.3+2.3.3+...+99.100.3\)

\(=1.2.3+2.3.\left(4-1\right)+3.4\left(5-2\right)+...+99.100\left(101-98\right)\)

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

\(=99.100.101\)

\(\Rightarrow A=\dfrac{99.100.101}{3}=333300\)