Find the radius of convergence of the series .
To find the radius of convergence \( R \) of the series \[ \sum a_n x^n \quad \text{where} \quad a_n = \frac{n!}{n^n}, \] we can use the Root Test or ________ ___ ____ ___ _____ _______ _____ ____.
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निम्नलिखित श्रेणी के अभिसरण की जाँच कीजिए :
Prove that the sequence (an)n∈N, where an = 32 / x2 + 22 , is Cauchy.
) मान लीजिए
जाँच की f, [-1,1] पर एकसमान सांतत्य है या नहीं।
Test the following series for convergence:
Which of the following statements are true or false? Give reasons for your answers in the form of a short proof or counter-example, whichever is appropriate:
i) Every infinite set is an open set.
ii) The negation of p^~qis p→q.
iii) -1 is a limit point of the interval ]-2,1].
iv) The necessary condition for a function f to be integrable is that it is continuous.
The function f: R→R defined by f(x) = |x-2|+|3-x is differentiable at x = 5.
सिद्ध कीजिए कि फलनों का अनुक्रम {fn} जहाँ
कॉशी समाकल परीक्षण द्वारा निम्नलिखित मूल्यांकन कीजिए :