$\frac{1}{3.4.5}$+$\frac{1}{4.5.6}$+$\frac{1}{5.6.7}$+…+$\frac{1}{30.31.32}$

0 bình luận về “$\frac{1}{3.4.5}$+$\frac{1}{4.5.6}$+$\frac{1}{5.6.7}$+…+$\frac{1}{30.31.32}$”

1. `1/(3.4.5)+ 1/(4.5.6) + 1/(5.6.7) +…+ 1/(30.31.32)`

   `= 1/2 .(2/(3.4.5) + 2/(4.5.6)+…+ 2/(30.31.32))`

   `=1/2 .( 1/(3.4) – 1/(4.5) + 1/(4.5) -1/ (5.6) +…+ 1/(30.31) – 1/(31.32))`

   `=1/2 .(1/(3.4) – 1/(31.32))`

   `=1/2 . (1/12 – 1/992)`

   `=1/2 . 245/2976`

   `=245/5952`

    

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2. Đặt `A=1/(3.4.5)+1/(4.5.6)+1/(5.6.7)+…+1/(30.31.32)`

   `⇒2A=2/(3.4.5)+2/(4.5.6)+2/(5.6.7)+…+2/(30.31.32)`

   `⇒2A=1/(3.4)-1/4.5+1/(4.5)-1/5.6+1/(5.6)-1/6.7+…+1/(30.31)-1/31.32`

   `⇒2A=1/(3.4)-1/31.32`

   `⇒2A=(245)/(2976)`

   `⇒A=(245)/(5952)`

   Vậy `A=(245)/(5952)`.

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