## A=1.2+2.3+3.4+….+1999.2000 B=1.1+2.2+3.3+…..+1999.1999 C=1.2.3+2.3.4+3.4.5+….+48.49.50

Question

A=1.2+2.3+3.4+….+1999.2000
B=1.1+2.2+3.3+…..+1999.1999
C=1.2.3+2.3.4+3.4.5+….+48.49.50

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2 tháng 2021-07-29T21:36:00+00:00 1 Answers 9 views 0

1. Giải thích các bước giải:

$A=1.2+2.3+3.4+..+1999.2000$

$\rightarrow 3A=1.2.3+2.3.3+3.4.3+..+1999.2000.3$

$\rightarrow 3A=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+..+1999.2000.(2001-1998)$

$\rightarrow 3A=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+..+1999.2000.2001-1998.1999.2000$

$\rightarrow 3A=1999.2000.2001$

$\rightarrow A=\dfrac{1999.2000.2001}{3}$

$B=1.1+2.2+3.3+..+1999.1999$

$\rightarrow B=1.(2-1)+2.(3-1)+3.(4-1)+..+1999.(2000-1)$

$\rightarrow B=1.2+2.3+3.4+..+1999.2000-(1+2+3+..+1999)$

$\rightarrow B=\dfrac{1999.2000.2001}{3}-\dfrac{1999.(1+1999)}{2}$

$\rightarrow B=\dfrac{1999.2000.2001}{3}-\dfrac{1999.2000}{2}$

$C=1.2.3+2.3.4+..+48.49.50$

$\rightarrow 4C=1.2.3.4+2.3.4.4+..+48.49.50.4$

$\rightarrow 4C=1.2.3.(4-0)+2.3.4.(5-1)+..+48.49.50.(51-47)$

$\rightarrow 4C=1.2.3.4-0.1.2.3.4+2.3.4.5-1.2.3.4+..+48.49.50.51-47.48.49.50$

$\rightarrow 4C=48.49.50.51$

$\rightarrow C=\dfrac{48.49.50.51}{4}$