Question

Tinh A = 1.2+2.3+3.4+...+n.(n+1)

Answer 1

Bài giải:

 

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + n(n +1)3

= 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ...+ n(n + 1)[(n + 2) - (n -1)]

= 1.2.3 + 2.3.4 - 2.3 + 3.4.5 - 2.3.4 + ... + n(n + 1)(n + 2) - n(n + 1)(n - 1)

= n(n + 1)(n + 2)

=> S N(N+1)(n+2)/3

 

Answer 2

3S = 1.2.3 + 2.3.3 + 3.4.3 + ... + n(n +1)3

= 1.2.(3 - 0) + 2.3.(4 - 1) + 3.4.(5 - 2) + ...+ n(n + 1)[(n + 2) - (n -1)]

= 1.2.3 + 2.3.4 - 2.3 + 3.4.5 - 2.3.4 + ... + n(n + 1)(n + 2) - n(n + 1)(n - 1)

= n(n + 1)(n + 2)

=> S = \(\frac{n\left(n+1\right)\left(n+2\right)}{3}\)

 

Answer 3

Mk suýt nữa biết !

Answer 4

mk k biết