数学达人来!两个小问题 1.对任意的正数n,1/[(n-1)(n+1)]={[1/(n-1)]-[1/(n+1)]}. 2.若(7n+4)/[n...数学达人来!两个小问题1.对任意的正数n,1/[(n-1)(n+1)]={[1/(n-1)]-[1/(n+1)]}.2.若(7n+4)/[n(n+2)]=A/n+B/(n+2),求A.B的值请写出解题步骤,谢谢!
2020-01-04
数学达人来!两个小问题 1.对任意的正数n,1/[(n-1)(n+1)]=___{[1/(n-1)]-[1/(n+1)]}. 2.若(7n+4)/[n...
数学达人来!两个小问题
1.对任意的正数n,1/[(n-1)(n+1)]=___{[1/(n-1)]-[1/(n+1)]}.
2.若(7n+4)/[n(n+2)]=A/n+B/(n+2),求A.B的值
请写出解题步骤,谢谢!
优质解答
1、1/(n-1)(n+1)=1/2 {[1/(n-1)]-[1/(n+1)]}.
事实上1/(n-a)(n-b)=1/(a-b)[1/(n-a)-1/(n-b)]
2、A/n+B/(n+2)=[(A+B)n+2A]/[n(n+2)]
则A+B=7,2A=4
所以A=2,B=5
1、1/(n-1)(n+1)=1/2 {[1/(n-1)]-[1/(n+1)]}.
事实上1/(n-a)(n-b)=1/(a-b)[1/(n-a)-1/(n-b)]
2、A/n+B/(n+2)=[(A+B)n+2A]/[n(n+2)]
则A+B=7,2A=4
所以A=2,B=5