Question

Tính B biết:

B=2*4+4*6+6*8+...+100*102

Answer 1

\(\text{B = 2.4 + 4.6 + 6.8 + .... +100.102}\)

\(\text{B = 2( 1.2 + 2.3 + 3.4 + ... + 50.51 )}\)

Đặt \(\text{A = 1.2 + 2.3 + 3.4 + ... + 50.51}\)

\(3A=1.2\left(3-0\right)+2.3\left(4-1\right)+...+50.51\left(52-49\right)\)

\(3A=1.2.3-0.1.2+2.3.4-1.2.3+...+50.51.52-49.50.51\)

\(3A=0.1.2+50.51.52\)

\(3A=50.51.52\)

\(3A=132600\)

\(A=\frac{132600}{3}=44200\)

\(\Rightarrow B=2.44200\)

\(\Rightarrow B=88400\)