1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)这道题该怎么做?

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1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)这道题该怎么做?1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x

1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)这道题该怎么做?
1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)这道题该怎么做?

1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)这道题该怎么做?
1/(x-1)(x-3)+1/(x-3)(x-5)+1/(x-5)(x-7)+...+1/(x-97)(x-99)
=(1/2)[1/(x-3)-1/(x-1)+1/(x-5)-1/(x-3)+...+1/(x-99)-1/(x-97)]
=(1/2)[-1/(x-1)+1/(x-99)]
=49/(x-1)(x-99)