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$^n\sqrt{2^n-n^2} = ?$

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#real-analysis #sequences-and-series #infinite-product
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Show that the common ratio between any two consecutive terms of a geometric sequence is a constant r.

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#sequences-and-series
81
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What is the equivalent of $f$ when $x$ approaches $1$?

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#real-analysis #sequences-and-series #power-series
157
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Proof Help: (Series) Bartle Exercise 9.3 Q 4

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#real-analysis #sequences-and-series #limits #proof-writing #cauchy-sequences
94
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$ (a_{n})_{n\in \mathbb{N}} $ , $ a_{0}=-1 $ , $a_{n+1}=2+\int_{a_{n}}^{1} e^{-x^2}dx$

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#calculus #sequences-and-series #definite-integrals
124
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The power series of $f(x)= \frac{1}{a-x}$

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#calculus #sequences-and-series #power-series #taylor-expansion
697
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evaluating definite integrals using power series, $\sqrt{1+x^4}$

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#calculus #sequences-and-series #definite-integrals #power-series
55
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Show that $S_N(x + y) > S_N(x) + S_N(y) - 1$

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#real-analysis #sequences-and-series #taylor-expansion
30
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Converging series and bounds on partial sum

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#sequences-and-series #convergence-divergence
79
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Showing the Taylor expansion converges to the function

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#real-analysis #sequences-and-series #analysis #derivatives #taylor-expansion
37
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proving/disproving the statements

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#calculus #sequences-and-series #convergence-divergence
1.6k
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conditionally convergence of $\{\cos(n)/\sqrt{n}\}$

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#real-analysis #sequences-and-series
52
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If $\limsup_{n} P^n(x,C) \le 1-\epsilon$ then the average of the transition probabilities cannot be tight.

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#real-analysis #sequences-and-series #analysis #probability-theory #limsup-and-liminf
93
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Determine if this series : $\sum_{n=1}^\infty e^{-\sqrt{(n+1)}}$ converges or diverges.

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#sequences-and-series
486
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Monotonicity in Alternating Series Test

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#real-analysis #sequences-and-series

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