Question

Tính:
\(C=1\cdot2\cdot3+2\cdot3\cdot4+3\cdot4\cdot5+4\cdot5\cdot6+5\cdot6\cdot7+6\cdot7\cdot8+...+98\cdot99\cdot100\)

Answer 1

C=2^3-2+3^3-3+...+99^3-99

=2^3+3^3+...+99^3-(2+3+...+99)

=(1+...+99)^2-1-4851

=(99*100/2)^2-4852

=24497648