An infinity-superscripted capital sigma often denotes—for 10 points—what mathematical object, the sum of an infinite sequence?
A property of these objects holds in a disc of radius "one-over the "lim sup" of the nth-root of the absolute value of c-sub-n." Analytic functions can be given by one of these objects. One of these objects was shown by Euler to equal "pi-squared over six," as the solution to the Basel Problem. For a k-times-differentiable function f, truncating one of these objects gives the best degree-k (*) polynomial approximation of f, according to Taylor's theorem. The terms "one-over-n" for natural numbers n comprise the "harmonic" one, which diverges. An infinity-superscripted capital sigma often denotes—for 10 points—what mathematical object, the sum of an infinite sequence?
A property of these objects holds in a disc of radius "one-over the "lim sup" of the nth-root of the absolute value of c-sub-n."
infinite series [accept more specific answers like power series, Taylor series, or harmonic series; accept infinite summations; prompt on just summations; do not accept or prompt on “sequences”] &lt;JR&gt;