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Arithmetic series, find the first 80 natural numbers which sum when divided by 31 has a remainder of 17

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#sequences-and-series #arithmetic
79
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Calculate the sum of first 45 numbers

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#sequences-and-series
138
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let define the "waved" factorial as $\prod_{i=1}^n (\text{if } \bmod(i,2)=={0\text{ or } 1}\text{ then } [2/i] \text{ else } [i])$

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#sequences-and-series #factorial #pi #infinite-product
34
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Why is $\lim_{n\rightarrow \infty } \frac{\sum_{i=1}^{n} 2^{1/n}}{n}$ equal to 1?

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#calculus #sequences-and-series #limits
56
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Partial sum of the sequence $\frac{X-n}{n}$

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#sequences-and-series
466
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Use Taylor's theorem to compute a quadratic approximation of $f : \mathbb{R}^2 \rightarrow \mathbb{R}$

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#sequences-and-series #taylor-expansion #nonlinear-optimization
107
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Discuss convergence of the series $\sum \left\{e-(1+\frac{1}{k})^k \right\}$

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#calculus #sequences-and-series
1.1k
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Alternative proof of Abel's Theorem for Uniform convergence of series of functions

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#real-analysis #sequences-and-series #analysis #convergence-divergence #uniform-convergence
346
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Partial sum of the sequence of combinations of 256

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#sequences-and-series
185
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What is the value of the infinite sum of $1+\frac{1}{3}+\frac{1.3}{3.6}+\frac{1.3.5}{3.6.9}+\frac{1.3.5.7}{3.6.9.12}....$

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#sequences-and-series
170
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Prove that if $x_n \leq y_n, \forall n$ then the same inequality holds for their limits, i.e. $x\leq y$

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#sequences-and-series #analysis
52
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What is the set of accumulation points of $a_{n} = \frac{2n^2}{7} - \left\lfloor { \frac{2n^2}{7}}\right\rfloor$?

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#sequences-and-series #limits
44
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Proving the Nested Interval property of $\mathbb{R}$

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#real-analysis #sequences-and-series
536
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Sum of $1+\frac{1\cdot 3}{6}+\frac{1\cdot 3 \cdot 5}{6 \cdot 8}+\cdots \cdots$

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#sequences-and-series #gamma-function #beta-function
63
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What is the value of this series?

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#sequences-and-series

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