Question

Tính:

a, A = 1 x 2 + 3 x 4 + 4 x 5 +....+ 15 x 16

b, A = 1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 + ....+ 15 x16 x 17

Answer 1

\(A=1.2+2.33.4+...+15.16\\ \Rightarrow3A=1.2.3+2.3.3+3.4.3+...+15.16.3\\ \Rightarrow3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+15.16.\left(17-14\right)\\ \Rightarrow3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+15.16.17-14.15.16\\ \Rightarrow3A=15.16.17\\ \Rightarrow A=\dfrac{15.16.17}{3}\\ \Rightarrow A=1360\)

Answer 2

\(b,A=1.2.3+2.3.4+...+15.16.17\\ \Rightarrow4A=1.2.3.4+2.3.4.4+...+15.16.17.4\\ \Rightarrow4A=1.2.3.4+2.3.4.\left(5-1\right)+...+15.16.17.\left(18-14\right)\\ \Rightarrow4A=1.2.3.4+2.3.4.5-1.2.3.4+...+15.16.17.18-14.15.16.17\\ \Rightarrow4A=15.16.17.18\\ \Rightarrow A=\dfrac{15.16.17.18}{4}\\ \Rightarrow A=18360\)