cho A=1/4.5+1/5.6+…+1/48.49+1/49.49 cho B=1/25+1/36+….+1/2401+1/2500 a, so sánh A và B b,CTR B<3/10

0 bình luận về “cho A=1/4.5+1/5.6+…+1/48.49+1/49.49 cho B=1/25+1/36+….+1/2401+1/2500 a, so sánh A và B b,CTR B<3/10”

1. Đáp án:a)A>B  b)đpcm

    

   Giải thích các bước giải:

   a) Ta có: B=1/25+1/36+…+1/2401+1/2500=1/5²+1/6²+…+1/49²+1/50²=1/5×5+1/6×6+…=1/49×49+1/50×50

   Ta có: 1/4×5>1/5×5

             1/5×6>1/6×6

             …………………….

             1/48×49>1/49×49

             1/49×50>1/50×50

   =>   1/4.5+1/5.6+…+1/48.49+1/49.50>1/5.5+1/6.6+…+1/49.49+1/50.50

   => A>B

   b)A=1/4.5+1/5.6+…+1/48.49+1/49.50=1/4-1/5+1/5-1/6+…+1/48-1/49+1/49-1/50=1/4-1/50=23/100

   3/10=30/100   23/100<30/100

   =>A<3/10  mà B<A

   => B<3/10

   =>đpcm

    

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