Question

Tính dãy số có quy luật

G = 1.2 + 2.3 + 3.4 + ... + 99 . 100 

Answer 1

\(G=1\cdot2+2\cdot3+3\cdot4+...+99\cdot100\)

\(=1\left(1+1\right)+2\left(1+2\right)+3\left(1+3\right)+...+99\left(1+99\right)\)

\(=\left(1^2+2^2+3^3+...+99^2\right)+\left(1+2+3+...+99\right)\)

\(=\dfrac{99\left(99+1\right)\left(2\cdot99+1\right)}{6}+\dfrac{99\cdot100}{2}\)

=328350+4950

=333300