Question

Find the values of x so that the series below converges. $$sum_{n=0}^{infty} frac{(x-7)^{n}}{4^{n}}$$ Give your answer in interval notation. ( , )

          Find the values of x so that the series below converges.

$$sum_{n=0}^{infty} frac{(x-7)^{n}}{4^{n}}$$

Give your answer in interval notation.
( , )

$Find the values of x so that the series below converges. sumn=0^infty frac(x-7)^n4^n Give your answer in interval notation. ( , )$

Added by Heidi V.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

Step 1

The given series is: $$\sum_{n=0}^{\infty} (x - 7)^n 4^n$$ Now, we can combine the terms $(x - 7)^n$ and $4^n$ to get: $$\sum_{n=0}^{\infty} \left((x - 7)4\right)^n$$ This is a geometric series with the common ratio $r = (x - 7)4$. For a geometric series to Show more…

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