Question

tinh nhanh

A=1*1+2*2+3*3+...+99*99+100*100

giup minh nhanh nha 

minh dang can gap 

ai giai nhanh nhat minh tik cho

 

Answer 1

A=1.1+2.2+3.3+...+99.99+100.100

3A=1.2.3+2.3.(4-1)+...99.100.(101-98)

3A=1.2.3+2.3.4-1.2.3+...+99.100.101-98.99.100

3A=99.100.101=999900

A= 999900:3=333300

Answer 2

\(A=1^2+2^2+3^2+...+100^2\)

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

\(\Rightarrow A=1.2-1+2.3-2+3.4-3+...+100.101-100\)

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

\(\Rightarrow A=\frac{100.101.102}{3}-\frac{\left(100+1\right)\left[\left(100-1\right):1+1\right]}{2}=\frac{100.101.102.2}{6}-\frac{101.100.3}{6}\)

\(\Rightarrow A=\frac{100.101\left(102.2-3\right)}{6}\)