1/（1*3）=(1 - 1/3)*1/2
1/(3*5)=(1/3 -1/5)*1/2
1/(5*7)=(1/5 -1/7)*1/2
.
1/(49*51)=(1/49 -1/51)*1/2
所以原式=（1- 1/3 +1/3- 1/5 +1/5 -1/7+.+ 1/49- 1/51）*1/2
=（1- 1/51）*1/2
=50/51 *1/2
=25/51
1/1×3+1/3×5+1/5×7+...+1/49×51=
2个回答
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