1 1 1 1 … 1 (分子)
-----+-------+------+-----+ -----+----- (分数线)
1*3 3*5 5*7 7*9 … 49*51 (分母)
1 1 1 1 … 1 (分子)
-----+-------+------+-----+ -----+----- (分数线)
1*3 3*5 5*7 7*9 … 49*51 (分母)
上述式子等于 1/2(1-1/3+1/3-1/5+1/5-1/7+....-1/49+1/49-1/51)
=1/2×(1-1/51)
=1/2×50/51
=25/51
结果就是这样啦
分母中两个因数相差2,拆解后再通分,就是: