Câu hỏi của Vũ Minh Hằng

Question

Tính

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

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

Phương Trâm · Accepted Answer

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

$A=1.2+1.2+2.3+2.2+3.4+3.2+...+99.100+99.2$

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

$A=333300+9900$

$A=343200$

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

$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 $

$\Rightarrow$ $B=4M=176800$Câu trả lời: $A = 1.4 + 2.5 + 3.6 + ...+ 99.102$