证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)其中1,2,3,n均为字母a的右下角的小数字.要步骤的(肯定的吧)一定要对的,对的话再加分(我至少懂一点的)
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/05 23:42:39
![证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)其中1,2,3,n均为字母a的右下角的小数字.要步骤的(肯定的吧)一定要对的,对的话再加分(我至少懂一点的)](/uploads/image/z/2492388-36-8.jpg?t=%E8%AF%81%E6%98%8E%E6%81%92%E7%AD%89%E5%BC%8Fa1%2Fa2%28a1%2Ba2%29%2Ba2%2Fa3%28a2%2Ba3%29%2B%E2%80%A6%E2%80%A6%2Ban%2Fa1%28an%2Ba1%29%3Da2%2Fa1%28a1%2Ba2%29%2Ba3%2Fa2%28a2%2Ba3%29%2B%E2%80%A6%E2%80%A6%2Ba1%2Fan%28an%2Ba1%29%E5%85%B6%E4%B8%AD1%2C2%2C3%2Cn%E5%9D%87%E4%B8%BA%E5%AD%97%E6%AF%8Da%E7%9A%84%E5%8F%B3%E4%B8%8B%E8%A7%92%E7%9A%84%E5%B0%8F%E6%95%B0%E5%AD%97.%E8%A6%81%E6%AD%A5%E9%AA%A4%E7%9A%84%EF%BC%88%E8%82%AF%E5%AE%9A%E7%9A%84%E5%90%A7%EF%BC%89%E4%B8%80%E5%AE%9A%E8%A6%81%E5%AF%B9%E7%9A%84%2C%E5%AF%B9%E7%9A%84%E8%AF%9D%E5%86%8D%E5%8A%A0%E5%88%86%28%E6%88%91%E8%87%B3%E5%B0%91%E6%87%82%E4%B8%80%E7%82%B9%E7%9A%84%EF%BC%89)
证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)其中1,2,3,n均为字母a的右下角的小数字.要步骤的(肯定的吧)一定要对的,对的话再加分(我至少懂一点的)
证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)
其中1,2,3,n均为字母a的右下角的小数字.
要步骤的(肯定的吧)
一定要对的,对的话再加分(我至少懂一点的)
证明恒等式a1/a2(a1+a2)+a2/a3(a2+a3)+……+an/a1(an+a1)=a2/a1(a1+a2)+a3/a2(a2+a3)+……+a1/an(an+a1)其中1,2,3,n均为字母a的右下角的小数字.要步骤的(肯定的吧)一定要对的,对的话再加分(我至少懂一点的)
利用:
a1/[a2(a1+a2)] = 1/a2-1/(a1+a2)
a2/[a3(a2+a3)] = 1/a3-1/(a2+a3)
...
an-1/[an(an-1+an)] = 1/an-1/(an-1+an)
an/[a1(an+a1)] = 1/a1-1/(an+a1)
所以等式左边=(1/a1+1/a2+...+1/an)-[1/(a1+a2)+1/(a2+a3)+...+1/(an+a1)]
再利用:
a2/[a1(a1+a2)] = 1/a1-1/(a1+a2)
a3/[a2(a2+a3)] = 1/a2-1/(a2+a3)
...
an/[an-1(an-1+an)] = 1/an-1-1/(an-1+an)
a1/[an(an+a1)] = 1/an - 1/(an+a1)
所以等式右边=(1/a1+1/a2+...+1/an)-[1/(a1+a2)+1/(a2+a3)+...+1/(an+a1)]
可见等式左右相等.