搜搜考试网两道计算题 求过程
来源：学生作业帮 编辑：搜搜考试网作业帮 分类：数学作业 时间：2024/06/16 15:50:11
两道计算题 求过程
1、1/3+1/15+1/35+1/63+1/99
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=1/2 (1-1/3+1/3-1/5+1/5……+1/9-1/11)
=1/2(1-1/11)
=5/11
2、(1+1/2)(1+1/4)……(1+1/10)(1-1/3)(1-1/5)……(1-1/9)
=(3/2)x(5/4)x(7/6)x(9/8)x(11/10)x(2/3)x(4/5)x(6/7)x(8/9)
=11/10
因为(1+1/2)(1-1/3)=(3/2)(2/3)=1 (1+1/4)(1-1/5)=(5/4)(4/5)=1等
=1/(1x3)+1/(3x5)+1/(5x7)+1/(7x9)+1/(9x11)
=1/2 (1-1/3+1/3-1/5+1/5……+1/9-1/11)
=1/2(1-1/11)
=5/11
2、(1+1/2)(1+1/4)……(1+1/10)(1-1/3)(1-1/5)……(1-1/9)
=(3/2)x(5/4)x(7/6)x(9/8)x(11/10)x(2/3)x(4/5)x(6/7)x(8/9)
=11/10
因为(1+1/2)(1-1/3)=(3/2)(2/3)=1 (1+1/4)(1-1/5)=(5/4)(4/5)=1等