$ frac{1}{2003.2002}$ - $ frac{1}{2002.2001}$ -...- $ frac{1}{3.2}$ -$ frac{1}{2.1}$

Question

anhthu · Answer

Đ&aacute;p &aacute;n:       ĐỀ 1 :        Ta c&oacute; :        `A = -1/(2003.2002) - 1/(2002.2001) - .... - 1/(3.2) - 1/(2.1)`       `= -(1/(1.2) + 1/(2.3) + .... + 1/(2001.2002) + 1/(2002.2003))`       `= -(1 - 1/2 + 1/2 - 1/3 + ... + 1/2001 - 1/2002 + 1/2002 - 1/2003)`       `= -(1 - 1/2003)`       `= -2002/2003`       ĐỀ 2 :        a c&oacute; :        `A = 1/(2003.2002) - 1/(2002.2001) - .... - 1/(3.2) - 1/(2.1)`       `= 1/(2002 . 2003) - (1/(1.2) + 1/(2.3) + .... + 1/(2001.2002))`       `= 1/(2002 . 2003)  - (1 - 1/2 + 1/2 - 1/3 + ... + 1/2001 - 1/2002)`       `= 1/(2002 . 2003) - (1 - 1/2002)`       `= 1/2002 - 1/2003 - 1 + 1/2002`       `= 1/1001 - 2004/2003`       `= 2003/2005003 - 2006004/2005003`       `= 2004001/2005003`       Giải th&iacute;ch c&aacute;c bước giải:

minhuyen · Answer

`1/(2003.2002)-1/(2002.2001)-.......-1/(2.1)`   `=1/(2002.2003)-(1/(1.2)+1/(2.3)+1/(3.4)+........+1/(2001.2002))`   `=1/(2002.2003)-(1-1/2002)`   `=1/(2002.2003)-1+1/2002`   `=1/2002-1/2003-1+1/2002`   `=-1000/1001-1/2003`

$\frac{1}{2003.2002}$ – $\frac{1}{2002.2001}$ -…- $\frac{1}{3.2}$ -$\frac{1}{2.1}$

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