Question
Find the radius of convergence of the series , where
.
Answer :
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Consider the power series (\sum a_n x^n) with (a_n=\dfrac{n!}{n^n}). The radius of convergence (R) is given by
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Related Questions
सिद्ध कीजिए कि प्रत्येक अभिसारी अनुक्रम कौशी होता है।
सीमाओं पर कौशी का द्वितीय प्रमेय लिखिए। इसे यह प्रदर्शित करने के लिए प्रयोग कीजिए कि हो।
Check whether the following sets are open or closed or neither:
(i)
(ii)
Prove that .
जाँच कीजिए कि अनुक्रम , जिसे इस प्रकार से परिभाषित किया जाता है:
, और
.
अभिसारी है या नहीं।
If an infinite series converges, then show that
.
State Bolzano-Weierstrass theorem. Use it to check whether the set:
has a limit point.