Question

B = 2.4 + 4.6 + 6.8 + ... + 98.100 + 100.102

Answer 1

\(B=2.4+4.6+6.8+...+98.100\)

\(B=2.\left(1.2\right)+2.\left(2.3\right)+2.\left(3.4\right)+...+2.\left(49.50\right)\)

\(B=2\left(1.2+2.3+3.4+....+49.50\right)\)

Đặt:

\(A=1.2+2.3+3.4+...+49.50\)

\(3A=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+49.50.\left(51-48\right)\)

\(3A=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+49.50.51-48.49.50\)

\(3A=49.50.51\)

\(A=\dfrac{49.50.51}{3}=41650\)

\(B=2A=41650.2=83300\)