Need to combine and simplify the following expression
1/(7-4*SQRT(3)) - 1/(4*SQRT(3)-SQRT(47)) + 1/(SQRT(47) - SQRT(46)) - 1/(SQRT(46)-3*SQRT(5)) +
1/(3*SQRT(5)-2*SQRT(11)) ......... - 1/(SQRT(5) - 2)
Simplifying a messy expression
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Chasyesker
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stapel_eliz
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Does the above mean the following?Need to combine and simplify the following expression
1/(7-4*SQRT(3)) - 1/(4*SQRT(3)-SQRT(47)) + 1/(SQRT(47) - SQRT(46)) - 1/(SQRT(46)-3*SQRT(5)) +
1/(3*SQRT(5)-2*SQRT(11)) ......... - 1/(SQRT(5) - 2)
Also, what is included in the ellipsis (the "dot dot dot") near the end? Is the pattern as follows (so, in particular, the sign on your last fraction should have been a "plus")?
When you reply, please show your work so far, and provide any rules,theorems, or other results from your class which you feel might be relevant. Thank you!
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Chasyesker
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Re: Simplifying a messy expression
That's correct. I don't have access to the radical symbols so sorry for the messiness. I got as far as figuring out the pattern. The problem as stated has a negative sign for the last term but I think you are correct that it s/b +. The assigment sheets have ben known to be a bit sloppy when it comes to exactness.
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maggiemagnet
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Re: Simplifying a messy expression
This might help a little:
-(n)}\, =\, {\sqrt{n+1}+\sqrt{n}})
So your fractions turn into:
^n ({\sqrt{n+1}+\sqrt{n}}))
The fractions start at n=48 and go to n=4.
\, -\, (\sqrt{48}+\sqrt{47})\, +\, (\sqrt{47}+\sqrt{46})\, -\, ...\, -\, (\sqrt{6}+\sqrt{5})\, +\, (\sqrt{5}+\sqrt{4}))
\, +\, (-\sqrt{47}+\sqrt{47})\, +\,... \, +\, (-\sqrt{5}+\sqrt{5})\, +\, \sqrt{4})
So it comes down to 7+2=9. That seemed too easy, though, so I checked in Wolfram Alpha, and got the same thing, so I guess it's right!
So your fractions turn into:
The fractions start at n=48 and go to n=4.
So it comes down to 7+2=9. That seemed too easy, though, so I checked in Wolfram Alpha, and got the same thing, so I guess it's right!
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Chasyesker
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Re: Simplifying a messy expression
Yep,
That's what I eventually got and like you it seemed to easy but I guess they are not always hard. Thanks for spotting the wrong sign in the problem on the last term. That's how the sign was shown on the handout so I am going to assume it was a typo. I wrote it all out by hand and it should be "+". Hopefully I won't have to argue with the teacher.
Thanks again.
That's what I eventually got and like you it seemed to easy but I guess they are not always hard. Thanks for spotting the wrong sign in the problem on the last term. That's how the sign was shown on the handout so I am going to assume it was a typo. I wrote it all out by hand and it should be "+". Hopefully I won't have to argue with the teacher.
Thanks again.