Question

tinhS:1*2+2*3+3*4+...+38*39+39*40

Answer 1

Ta có :

\(S=1.2+2.3+....+39.40\)

\(\Leftrightarrow3S=1.2.\left(3-0\right)+2.3.\left(4-1\right)+....+39.40.\left(41-38\right)\)

\(\Leftrightarrow3S=1.2.3-0.1.2+2.3.4-1.2.3+.....+39.40.41-38.39.40\)

\(\Leftrightarrow3S=39.40.41\)

\(\Leftrightarrow S=\frac{39.40.41}{3}=21320\)

Answer 2

Ta có :

S=1X2+2X3+.........+38X39+39X40

=> 3S = 1X2X3+2X3X3+........+38X39X3+39X40X3

=>3S = 1X2X(3-0)+2X3X(4-1)+.........+38X39X(40-37)+39X40X(41-38)

=> 3S = 1X2X3-0X1X2+2X3X4-1X2X3+...+38X39X40-37X38X39 +39X40X41-38X39X40

=>3S = 39X40X41=63960

=>S = 63960:3

S = 21320

Answer 3

21320