$\frac{1}{3}$ +$\frac{2}{ 3^{2} }$ +$\frac{3}{ 3^{3} }$ +…+$\frac{100}{ 3^{100} }$

0 bình luận về “$\frac{1}{3}$ +$\frac{2}{ 3^{2} }$ +$\frac{3}{ 3^{3} }$ +…+$\frac{100}{ 3^{100} }$”

1. Đặt A = `1/3+2/3^2+3/3^3 +…+100/3^100`

   `⇒3A= 1+2/3+3/3^2 +…+100/3^99`

   `⇒3A-A=2A=1+1/3+1/3^2+….+1/3^99-1/3^100`

   `⇒A=(1+1/3+1/3^2+….+1/3^99-1/3^100)/2`

    Đặt  `1+1/3+1/3^2+….+1/3^99=B`

   `⇒3B= 3+1+1/3+….+1/3^98`

   `⇒3B-B=2B=3-1/3^99`

   `⇒B=(3-1/3^99)/2`

   `⇒A=((3-1/3^99)/2-1/3^100)/2`

    

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