Question

[Phạm Thị Quỳnh Anh]

Tính: \(1+2+3^2+4^2+...+99^2+100^2\)

Làm giúp mk. Mk đang cần gấp! THANK YOU!

Answer 1

[Nguyễn Minh Đăng]

Ta có: \(1+2^2+3^2+4^2+...+99^2+100^2\) (đề đúng)

\(=1\left(2-1\right)+2\left(3-1\right)+3\left(4-1\right)+...+99\left(100-1\right)+100\left(101-1\right)\)

\(=\left(1.2+2.3+3.4+...+99.100+100.101\right)-\left(1+2+3+...+100\right)\)

\(=\frac{1.2.3+2.3.3+...+100.101.3}{3}-\frac{\left(100+1\right)\left[\left(100-1\right)\div1+1\right]}{2}\)

\(=\frac{1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+100.101.\left(102-99\right)}{3}-5050\)

\(=\frac{1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-...-99.100.101+100.101.102}{3}-5050\)

\(=\frac{100.101.102}{3}-5050\)

\(=343400-5050\)

\(=338350\)