Tính nhanh 2/3 + 14/15 + 34/35 + 62/63 + 98/99

1 bình luận về “Tính nhanh 2/3 + 14/15 + 34/35 + 62/63 + 98/99”

1. 2/3 + 14/15 + 34/35 + 62/63 + 98/99

   = (1 – 1/3) + (1- 1/15) + (1 – 1/35) + (1 – 1/63) + (1 – 1/99)

   = (1 – 1/(1xx3) ) + (1 – 1/(3xx5) ) + (1 – 1/(5xx7) ) + (1 – 1/(7xx9) ) + (1 – 1/(9xx11) )

   = (1+1+1+1+1) – (1/(1xx3) + 1/(3xx5) + 1/(5xx7) + 1/(7xx9) + 1/(9xx11))

   = 5 – 1/2 xx (2/(1xx3) + 2/(3xx5) + 2/(5xx7) + 2/(7xx9) + 2/(9xx11) )

   = 5 – 1/2 xx (1- 1/3 + 1/3 – 1/5 + 1/5 – 1/7 + 1/7 – 1/9 + 1/9 – 1/11)

   = 5 – 1/2 xx (1-1/11)

   = 5 – 1/2 xx 10/11

   = 5 – 5/11

   = 50/11

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