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Originally Posted by roshanhero Here is a hint:
Originally Posted by Plato Here is a hint:
I have reached upto here Now, What should I do?
Originally Posted by roshanhero I will denote , and take natural logarithm from both sides.
See what happens...
Let . Since , the limit of the sequence is . Maybe it will be more interesting to look at .
Another tricky way is to test the convergence of the corresponding series
The series converges by the Ratio Test.
I simply have to find the limit as n tends to infinity, I don't have to use any methods of tests of convergence here
According to my way...
Now just apply the sandwich rule.
Originally Posted by roshanhero Note that is the Binomial Coefficient , which is a positive integer.
We have the equality: .
But and therefore . The strict inequaliy shows that the integers tend to infinity as gets larger.
To AlsoSprachZarathusra, there's no need to take logarithms to get the last two lines!
for large n,
Originally Posted by roshanhero melese reminded me...
Originally Posted by Also sprach Zarathustra According to my way...
Now just apply the sandwich rule. How did u get as lower and upper bounds?
Originally Posted by roshanhero How did u get as lower and upper bounds?
Hello, roshanhero! . .
Divide top and bottom by . .
As gets larger, the sequence approximates . . a geometric sequence with common ratio
Therefore, the limit of the sequence is zero.
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