爱管闲事1234
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1/3+1/15+1/35.....................+1/(17*19)
=1/(1*3)+1/(3*5)+1/(5*7)++....................+1/(17*19)
=(1-1/3)/2+(1/3-1/5)/2+(1/5-1/7)/2+..................+(1/17-1/19)
=(1-1/3+1/3-1/5+1/5-1/7+1/7-.............................+1/17-1/19)/2
=(1-1/19)/2
=(18/19)/2
=9/19
1年前
2
