Asymptotic behavior of partial sums of a series of probabilities of large deviationsLet {X k } ∞ k=1 be a sequence of independent, symmetric random variables with characteristic functions f k (t), The asymptotic behavior of the sum (for arbitrary ɛ > 0) is investigated under the ...
Partial Sum of a Series: A series is a sum of the terms of a sequence. A series is said to be convergent, divergent or oscillate according as the sequence of partial sums of the series is convergent, divergent or oscillate. The limit of both ...
Partial sums of a series of constants are graphed, and the sum of the series is obtained as the limit of the sequence of partial sums. Note: In Maple 2018, context-sensitive menus were incorporated into the new Maple Context Panel, located on the right side of the Maple window. If you...
V. Nestoridis conjectured that if $\\\Omega$ is a simply connected subset of $\\\mathbb{C}$ that does not contain $0$ and $S(\\\Omega)$ is the set of all functions $f\\\in \\\mathcal{H}(\\\Omega)$ with the property that the set $\\\left\\\{T_N(f)(z)\\\coloneqq...
We need to find 10 partial sums of the series. ∑n=1∞16(−3)n We have the series: {eq}\sum...Become a member and unlock all Study Answers Start today. Try it now Create an account Ask a question Our experts can answer your tough homew...
Let us define things a little better now:A Sequence is a set of things (usually numbers) that are in order.A Partial Sum is the sum of part of the sequence.The sum of infinite terms is an Infinite Series. And Partial Sums are sometimes called "Finite Series"....
Here is the unique root of the equation It is proved that the order in this estimate cannot be improved. Various generalizations of this result are also obtained.Bibliography: 10 titles. 关键词: NONNEGATIVE PARTIAL SUMS COSINE-SERIES DOI: 10.1070/SM1994v077n02ABEH003443 被引量: 6 年份...
From the graph and the table, it seems that the series converges to -2 . In fact, it is a geometric series with a=-2.4 and r=-1/5, so its sum is ∑limits_(n=1)^∞ (12)((-5)^n)=(-2.4)(1-(-1/5))=(-2.4)(1.2)=-2. Note that the dot corresponding to n=1 is part...
摘要: We give sharp lower estimates for the partial sums of the Fourier series sinx+fraccos2x2+fracsin3x3+fraccos4x4+,sin x+frac{cos2x}{2}+frac{sin 3x}{3}+frac{cos 4x}{4}+cdots关键词: trigonometric polynomials inequalities DOI: 10.1007/s00365-006-0665-0 被引量: 19 ...
The partial sums of the series ∑_(n=0)^∞ x^n definitely do not converge to f(x)=1((1-x)) for x ≥q 1, since f is undefined at x=1 and negative on (1, ∞), while all the partial sums are positive on this interval. The partial sums also fail to converge to f for x...