How to evaluate this limit

Subhotosh Khan said:
You mean you do not know how to continue??!!
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No, not with your method :( . My first thought was to multiply by conjugates.
I asked my 10th grade daughter what is infinity - 2*inf + inf expecting her to say 0 but instead she replied inf is not a number so you can't add or subtract them. Thankfully she did not get her math ability from me.
 
Math_newbie said:
View attachment 23311

I want to find this limit but i can't figure it out.Any suggestions?
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I would suggest this rationalization;
\(\left[ {\sqrt {n + 3} - 2\sqrt {n + 4} + \sqrt {n + 5} } \right]\left( {\frac{{\left[ {\sqrt {n + 3} + 2\sqrt {n + 4} - \sqrt {n + 5} } \right]}}{{\left[ {\sqrt {n + 3} + 2\sqrt {n + 4} - \sqrt {n + 5} } \right]}}} \right)\)
SEE HERE
 
Jomo said:
No, not with your method :( . My first thought was to multiply by conjugates.
I asked my 10th grade daughter what is infinity - 2*inf + inf expecting her to say 0 but instead she replied inf is not a number so you can't add or subtract them. Thankfully she did not get her math ability from me.
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in my 1st yr. calculus Calculus, I was taught Taylor's series! Think a bit and you will see the light. May be your daughter can teach you that one or Google it!!

btw you don't have to go to infinity!!
 
Subhotosh Khan said:
in my 1st yr. calculus Calculus, I was taught Taylor's series! Think a bit and you will see the light. May be your daughter can teach you that one or Google it!!
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Yes, but these type of limits come before Taylor's series.
 
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