1what is x in the second one..?
1) Find \lim_{x\rightarrow0}{{\left( \frac{1^{x}+2^{x}+3^{x}+.....+n^{x}}{n}\right)^{1/x}}}
2) Find \lim_{n\rightarrow(infinity)}\frac{1^{k}+2^{k}+3^{k}+........+n^{k}}{n^{k+1}}
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12 Answers
1the first one...
eL... where L = \lim_{x\rightarrow0}{{\left( \frac{1^{x}+2^{x}+3^{x}+.....+n^{x}-n}{nx}\right)}}}
= ln(n!)n......
I think i made some mistake . pls tell me.
13)Find \lim_{n\rightarrow(infinity)}\frac{\left( n!^{1/n}\right)}{n}
1@philip--
ur answer to 1st ques is correct!!
did u try IInd one?
1@debo-
No, u cant say that.....coz n→∞ here.
& u don't know the value of k.
So, u cant say anything like that........!!