Question

A = 1*2*3+3*4*5+5*6*7+...+99*99*100

Answer 1

\(A=1.2.3+3.4.5+......+99.100.101\)

\(\Leftrightarrow A=1.3\left(5-3\right)+3.5\left(7-3\right)+......+99.101\left(103-3\right)\)

\(\Leftrightarrow A=\left(1.3.5+3.5.7+.....+99.101.103\right)-\left(1.3.3+3.5.3+......+99.101.3\right)\)

\(\Leftrightarrow A=\left(15+99.101.103.105\right):8-3\left(1.3+3.5+......+99.101\right)\)

\(\Leftrightarrow A=13517400-3.171650\)

\(\Leftrightarrow A=13517400-514950\)

\(\Leftrightarrow A=13002450\)

Answer 2

bấm trên máy tính 100! là xong