第1个等式:a1=1/1×3=1/2×(1-1/3); 第2个等式:a2=1/3×5=1/2×(1/3-1/5)第3个等式:a3=1/5×7=1/2×(1/5-1/7);第4个等式:a4=1/7×9=1/2×(1/7-1/9);.求a1+a2+a3+a4+...+a100的
来源:学生作业帮助网 编辑:作业帮 时间:2024/08/16 12:14:01
![第1个等式:a1=1/1×3=1/2×(1-1/3); 第2个等式:a2=1/3×5=1/2×(1/3-1/5)第3个等式:a3=1/5×7=1/2×(1/5-1/7);第4个等式:a4=1/7×9=1/2×(1/7-1/9);.求a1+a2+a3+a4+...+a100的](/uploads/image/z/7834795-43-5.jpg?t=%E7%AC%AC1%E4%B8%AA%E7%AD%89%E5%BC%8F%EF%BC%9Aa1%3D1%EF%BC%8F1%C3%973%3D1%EF%BC%8F2%C3%97%EF%BC%881%EF%BC%8D1%EF%BC%8F3%EF%BC%89%EF%BC%9B+%E7%AC%AC2%E4%B8%AA%E7%AD%89%E5%BC%8F%EF%BC%9Aa2%3D1%EF%BC%8F3%C3%975%3D1%EF%BC%8F2%C3%97%EF%BC%881%EF%BC%8F3%EF%BC%8D1%EF%BC%8F5%EF%BC%89%E7%AC%AC3%E4%B8%AA%E7%AD%89%E5%BC%8F%EF%BC%9Aa3%3D1%EF%BC%8F5%C3%977%3D1%EF%BC%8F2%C3%97%EF%BC%881%EF%BC%8F5%EF%BC%8D1%EF%BC%8F7%EF%BC%89%EF%BC%9B%E7%AC%AC4%E4%B8%AA%E7%AD%89%E5%BC%8F%EF%BC%9Aa4%3D1%EF%BC%8F7%C3%979%3D1%EF%BC%8F2%C3%97%EF%BC%881%EF%BC%8F7%EF%BC%8D1%EF%BC%8F9%EF%BC%89%EF%BC%9B.%E6%B1%82a1%2Ba2%2Ba3%2Ba4%2B...%2Ba100%E7%9A%84)
第1个等式:a1=1/1×3=1/2×(1-1/3); 第2个等式:a2=1/3×5=1/2×(1/3-1/5)第3个等式:a3=1/5×7=1/2×(1/5-1/7);第4个等式:a4=1/7×9=1/2×(1/7-1/9);.求a1+a2+a3+a4+...+a100的
第1个等式:a1=1/1×3=1/2×(1-1/3); 第2个等式:a2=1/3×5=1/2×(1/3-1/5)
第3个等式:a3=1/5×7=1/2×(1/5-1/7);
第4个等式:a4=1/7×9=1/2×(1/7-1/9);
.
求a1+a2+a3+a4+...+a100的值.
第1个等式:a1=1/1×3=1/2×(1-1/3); 第2个等式:a2=1/3×5=1/2×(1/3-1/5)第3个等式:a3=1/5×7=1/2×(1/5-1/7);第4个等式:a4=1/7×9=1/2×(1/7-1/9);.求a1+a2+a3+a4+...+a100的
a1+a2+a3+a4+...+a100
=1/2×(1-1/3)+1/2×(1/3-1/5)+1/2×(1/5-1/7)+.+1/2×【1/(2×100-1)-1/(2×100+1)】
=1/2【1-1/3+1/3-1/5+.+1/(2×100-1)-1/(2×100+1)】
=1/2(1-1/201)
=1/2×(200/201)
=100/201
设bn=1/(2n-1)
由题目得:an=(1/2)X(bn-b(n-1))
所以a1+a2+a3+........+a100=(1/2)(1-(1/3)+(1/3)-(1/5)+(1/5)+......+(1/99)-(1/201))
=(1/2)(1-(1/201))
...
全部展开
设bn=1/(2n-1)
由题目得:an=(1/2)X(bn-b(n-1))
所以a1+a2+a3+........+a100=(1/2)(1-(1/3)+(1/3)-(1/5)+(1/5)+......+(1/99)-(1/201))
=(1/2)(1-(1/201))
=(1/2)X(200/201)
=100/201
收起