Question

Tinh gia tri cua A biet 1.2.3+2.3.4+3.4.5+......+98.99+99.100

Answer 1

Bạn ghi bị lộn đề rồi, hai số cuối phải là \(97.98.99\)và \(98.99.100\)

\(4A=1.2.3.4+2.3.4.4+3.4.5.4+...+97.98.99.4+98.99.100.4\)

\(=1.2.3.4+2.3.4\left(5-1\right)+3.4.5\left(6-2\right)+...+97.98.99\left(100-96\right)+98.99.100.\left(101-97\right)\)

\(=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+...+98.99.100.101-97.98.99.100\)

\(=98.99.100.101=97990200\Rightarrow A=\frac{97990200}{4}=24497550\)