Find the Radius of Convergence and the Interval of Convergence $$\sum _ { n = 0 } ^ { \infty } \left( \frac { n x } { 6 } \right) ^ { n }$$

question 100

Short Answer

Find the radius of convergence and the interval of convergence of the power series.
$$\sum _ { n = 0 } ^ { \infty } \left( \frac { n x } { 6 } \right) ^ { n }$$

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Definitions:

Ossicles

The three small bones in the middle ear that transmit sound vibrations from the eardrum to the inner ear.

Timbre

The quality of a sound that distinguishes it from other sounds of the same pitch and volume.

Amplitude

The height or magnitude of a wave signal, illustrating the intensity or level of fluctuation.

Pitch

The perception of how high or low a sound is, fundamentally related to the frequency of the sound wave.