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

Answers ( )

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    2021-07-29T21:37:37+00:00

    Giải thích các bước giải:

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

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

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

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

    $\rightarrow 3A=1999.2000.2001$ 

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

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

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

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

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

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

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

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

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

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

    $\rightarrow 4C=48.49.50.51$

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

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