chứng minh rằng 1/6+1/66+1/176+…+1/(5n+1)(5n+6)=n+1/5n+6

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1. 1/6+1/66+1/176+…+1/(5n+1)(5n+6) = n+1/5n+6

   = 1/5 . ( 5/1.6 + 5/6 .11 + 5/11.16 + ….+ 5/(5n+1)(5n+6)

   =1/5 . (1 − 1/6 + 1/6 − 1/11 + 1/11 − 1/16 +...+ 1/5n+1 − 1/5n+6)

   = 1/5 . ( 1- 1/5n+6 )

   = 1/5 . ( 5n+5/5n+6 ) 

   = n+1/5n+6 (đpcm)

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2. Đáp án:

   `-`

   Giải thích các bước giải:

   `1/6+1/66+1/176+…+1/((5n+1)(5n+6))`

   `=1/1.6+1/6.11+1/11.16+…+1/((5n+1)(5n+6))`

   `=1/5(5/1.6+5/6.11+5/11.16+…+5/((5n+1)(5n+6)))`

   `=1/5(1-1/6+1/6-1/11+1/11-1/16+…+1/(5n+1)-1/(5n+6))`

   `=1/5(1-1/(5n+6))`

   `=1/5((5n+6)/(5n+6)-1/(5n+6))`

   `=1/5*(5n+5)/(5n+6)`

   `=(n+1)/(5n+6)`

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