Question

S = 1*2+2*3+3*4+.....+38*39+39*40

Answer 1

S = 1 x 2 + 2 x 3 + 3 x 4 + ... + 38 x 39 + 39 x 40

Ta có

S=1.2+2.3+....+39.40S=1.2+2.3+....+39.40

⇒3S=1.2(3−0)+2.3(4−1)+....+39.40(41−38)⇒3S=1.2(3−0)+2.3(4−1)+....+39.40(41−38)

⇒3S=1.2.3−0.1.2+2.3.4−1.2.3+....+39.40.41−38.39.40⇒3S=1.2.3−0.1.2+2.3.4−1.2.3+....+39.40.41−38.39.40

⇒S=39.40.413⇒S=39.40.41/3

=> S = 21320

Vậy S=21320

Answer 2

\(S=1.2+2.3+...+38.39\)

\(\Rightarrow3S=1.2\left(3-0\right)+2.3\left(4-1\right)+...+39.40\left(41-38\right)\)

\(\Rightarrow3S=1.2.3-0.1.2+2.3.4-1.2.3+...+39.40.41-38.39.40\)

\(\Rightarrow S=\frac{39.40.41}{3}\)

\(\Rightarrow S=21320\)