3分之1加5分之1加7分之1加9分之1,分母为等差数列的分数和怎么计算

2024-12-28 07:49:07
推荐回答(2个)
回答1:

1/3+1/5+1/7+...1/(2n+1)
=1+(1-1/3+1/3-1/5+1/5…-1/2n)*2
=1+(1-1/2n)*2
=1+2-1/n
=3-1/n

回答2:

1/3+1/5+1/7+1/9
=105/315+63/315+45/315+35/315
=248/315

9/8-8/7-7/6-6/5-5/4-4/3-3/2-2/1
=(1+1+1+1+1+1+1+1)-1/8-1/7-1/6-1/5-1/4-1/3-1/2
=248/315