Question

Tính

A = 1.4 + 2.5 + 3.6 + ...+ 99.102

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

Answer 1

\(A = 1.4 + 2.5 + 3.6 + ...+ 99.102\)

\(A=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2\)

\(A=(1.2+2.3+3.4+...+99.100)+2.(1+2+3+...+99)\)

\(A=333300+9900\)

\(A=343200\)

\(B = 2.4 + 4.6 + 6.8 + ....+ 98.100 + 100.102\)

\(B=(1.2)(2.2)+(2.2)(3.2)+...+(50.2)(51.2) \)

\(B=4(1.2+2.3+...+50.51) \)

\(M= 1.2+2.3+...+50.51 \)

\(3M=1.2.3+2.3.(4-1)+...+50.51.(52-49) \)

\(=1.2.3+2.3.4-1.2.3+...+50.51.52-49.50.51 \)

\(= 50.51.52\)

\(=132600 \)

\(\Rightarrow\)\(M=44200 \)

\(\Rightarrow\) \(B=4M=176800\)