Question

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

原式是9分之8减8分之7加7分之6减6分之5加5分之4减4分之3加3分之2减2分之1

Answer 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

Answer 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