Question

Tính tổng:

\(S=1.2+2.3+3.4+4.5+.....+99.100\)

Answer 1

Ta có: \(S=1.2+2.3+3.4+...+99.100\)

\(\Rightarrow3S=1.2.3+2.3.3+3.3.4+....+99.100.3\)

\(\Rightarrow3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)....99.100.\left(101-98\right)\)

\(\Rightarrow3S=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+99.100.101-98.99.100\)

\(\Rightarrow3S=99.100.101\)

\(\Rightarrow S=\frac{99.100.101}{3}=\frac{999900}{3}=333300\)

Answer 2

S=  1.2 + 2.3 +... + 99.100

=>S= \(\frac{99.100.101}{3}\)=333300

Answer 3

   \(S=1.2+2.3+3.4+4.5+...+99.100\)

\(3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

\(3S=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

Answer 4

S=1*2+2*3+3*4+...+99*100

3S=1*2*3+2*3*(4-1)+3*4*(5-2)+...+99*100*(101-98)

3S=1*2*3+2*3*4-1+...+99*100*101-98

3S=99*100*101

S=333300

Answer 5

3S= 1 x 2 x 3 + 2 x 3 x 3 + 3 x 4 x 3 + 4 x 5 x 3 + .....+ 99 x 100 x 3

3S= 1 x 2 x 3 + 2 x 3 x( 4-1) + 3 x 4 x ( 5-2)  + .......+ 99 x 100 x ( 101- 98)

3S= 1 x 2 x 3 + 2x 3 x4 - 1 x 2 x 3 + 3 x 4 x 5 - 2 x 3x 4 +......+ 99 x 100 x 101 - 98 x 99 x 100

3S= 1 x 2 x 3 - 1 x 2 x 3 + 2 x 3 x 4 - 2 x 3 x 4 + ......+ 99 x 100 x 101

3S= 99 x 100 x 101 = 999900

=> S = 999900 : 3 = 333300

      Vậy S = 333300

Answer 6

\(S=1.2+2.3+3.4+4.5+...+99.100\)

\(3S=1.2.3+2.3.3+3.4.3+...+99.100.3\)

\(3S=1.2.3+2.3.\left(4-1\right)+...+99.100.\left(101-98\right)\)

\(3S=99.100.101=\frac{999900}{3}=333300\)