Proof

Very nice work!

[MATH]\frac{1}{a^2}+\frac{1}{a^2x^2}+\frac{1}{a^2(x+1)^2}\\ =\dfrac{1}{a^2}\left(1+\dfrac{1}{x^2}+\dfrac{1}{(x+1)^2}\right)\\ =\dfrac{1}{\big(ax(x+1)\big)^2}\big(\big(x(x+1)\big)^2+(x+1)^2+x^2\big)\\ =\dfrac{1}{\big(ax(x+1)\big)^2}\big(\big(x(x+1)\big)^2+2x(x+1)+1\big)\\ =\dfrac{1}{\big(ax(x+1)\big)^2}\big(x(x+1)+1\big)^2[/MATH]
 
Brilliant Lex! This is a very nice question to optimise!

@Thales12345 please continue to post in this thread if you are still struggling. I would recommend that you continue on the original proposed path because you were VERY close to a solution. Hopefully post #15 will have been helpful to you. And don't feel that you have to invest a lot of time into working out how the quicker solutions work if you are struggling with this (if you decide to use one of them in your homework, make sure that you understand how it works and where the substitutions come from).
 
Cubist said:
Brilliant Lex! This is a very nice question to optimise!

@Thales12345 please continue to post in this thread if you are still struggling. I would recommend that you continue on the original proposed path because you were VERY close to a solution. Hopefully post #15 will have been helpful to you. And don't feel that you have to invest a lot of time into working out how the quicker solutions work if you are struggling with this (if you decide to use one of them in your homework, make sure that you understand how it works and where the substitutions come from).
Click to expand...
I started all over again with no substitutions within the exercise and that method is very parallel to #16. (this exercise is not homework, math is just one of my hobbies. This forum is very helpful, I wouldn't know where else to ask for help!)
 
You must log in or register to reply here.
Top