anonymous
  • anonymous
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Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\lim_{n \rightarrow \infty} [(1+1/ n^2)(1+2^2/n^2)......(1+n^2/n^2)]^{1/n}\]
anonymous
  • anonymous
why dont u try taking log..
anonymous
  • anonymous
i dont know how to do it

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anonymous
  • anonymous
if we simply put n=infinity result comes out to be \[1^{0}\]
anonymous
  • anonymous
is it an indeterminate form?
anonymous
  • anonymous
take log on both sides ln L = 1/n x sigma ln (1 + r^2/n^2)
anonymous
  • anonymous
take r/n = x, 1/n= dx
anonymous
  • anonymous
hence ln L = ln(1 + x^2)dx from 0 to 1
anonymous
  • anonymous
now use integral by parts to integrate this
anonymous
  • anonymous
is it an indeterminate form? 1^0
anonymous
  • anonymous
i told u..did u get it??????????????????????????/
anonymous
  • anonymous
deeprony? r u getting it?
anonymous
  • anonymous
i didnt understand what you said
anonymous
  • anonymous
see ill tell u the general method whenever u hav \[\sum_{0}^{\infty}f(r/n) \times 1/n\]
anonymous
  • anonymous
yes.. what do i do?
anonymous
  • anonymous
then put r/n = x and 1/n = dx
anonymous
  • anonymous
so u hav \[\int\limits_{0}^{1}f(x)dx\]
anonymous
  • anonymous
samjhe??
anonymous
  • anonymous
yea but why did u set the upper limit to 1??
anonymous
  • anonymous
when r=n then r/n is 1 isnt it/?
anonymous
  • anonymous
oh yes.. i get it now...
anonymous
  • anonymous
\[given=\lim_{n \rightarrow \infty} e^{\frac{\ln (1+\frac{1}{n^2})+...+\ln(1+\frac{n^2}{n^2})}{n}}\] apply l hospitals rule.
anonymous
  • anonymous
please i am having a doubt if we directly put n=infinity then the limit is coming out to be 2^0 is this an inderminate form???
anonymous
  • anonymous
its coming infinity^0
anonymous
  • anonymous
y so saubhik n^2 is in the denominator as n tends to infinity 1/n^2 , 2/n^2 ,... becomes 0
anonymous
  • anonymous
see the last term its 1+n^2/n^2. as n -> infty then thus term tends to infty. understood?
anonymous
  • anonymous
cancel the n^2 last term comes out to be 2
anonymous
  • anonymous
wow wow man!!! Mankind has not been able to understand till today what is infty/infty and yet u claim its 1!
anonymous
  • anonymous
ok my bad i should have been more careful
anonymous
  • anonymous
hey him r u der?
anonymous
  • anonymous
get it?
anonymous
  • anonymous
yea.. it worked out..=)

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