Math Problem Statement
if S=1/4^0+3/4^1+6/4^2+10/4^3+15/4^4+…, find ^3sqrtS
Solution
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Math Problem Analysis
Mathematical Concepts
Series
Geometric Series
Power Series
Cube Root
Formulas
T_n = \frac{n(n+1)}{4^n}
\sum_{n=0}^{\infty} \frac{n}{x^n} = \frac{x}{(1-x)^2}
\sum_{n=0}^{\infty} \frac{n^2}{x^n} = \frac{x(1+x)}{(1-x)^3}
S = \sum_{n=0}^{\infty} \frac{n(n+1)}{4^n}
\sqrt[3]{S}
Theorems
Geometric Series Formula
Sum of Power Series
Suitable Grade Level
Grade 11-12 / College level