Find the Maclaurin series of the function f(x)=ln(1?5x) Chocse the Maclaurin series. ln(1?5x)=??=1??5n(?1)?1x5n?ln(1?5x)=?=?1??n(?1)n?15nxn?ln(1?5x)=??n=1??5n54xn?ln(1?5x)=??n=1??n5?xn?? Identify the interval on which the series is valid. (Give your amiwer as an interval in tho form (?,?). Use the symbot oo for infinity, u for combining inservals, solutionspile.com

Question

Find the Maclaurin series of the function

f (x) = ln (1 ? 5 x)

Chocse the Maclaurin series.

ln (1 ? 5 x) = ?_{? = 1}^{?} \frac{( ? 1 ) ^{? 1} x ^{5 n}}{5 n} ln (1 ? 5 x) = ?_{= ? 1}^{?} \frac{( ? 1 ) ^{n ? 1} 5 ^{n} x ^{n}}{n} ln (1 ? 5 x) = ? ?_{n = 1}^{?} \frac{5 ^{4} x ^{n}}{5 n} ln (1 ? 5 x) = ? ?_{n = 1}^{?} \frac{5 ^{?} x ^{n}}{n}

Identify the interval on which the series is valid. (Give your amiwer as an interval in tho form

(?, ?)

. Use the symbot oo for infinity,

u

for combining inservals, and an appropriate type of parenthesis "

(,, y^{?}, " [7,]^{?}

depending on whether the interval is open or closed. Euler

?

if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where meded)

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