Answer
$0.9856$
Work Step by Step
The given series is $\Sigma_{n=1}^\infty \dfrac{(-1)^{n+1}}{n^6}$
The sums of the given series are as follows:
$S_1=\Sigma_{n=1}^3 \dfrac{(-1)^{n+1}}{n^6} \approx 9.85747$
$S_2=\Sigma_{n=1}^4 \dfrac{(-1)^{n+1}}{n^6} \approx 9.85502$
$S_3=\Sigma_{n=1}^5 \dfrac{(-1)^{n+1}}{n^6} \approx 9.85567$
$S_4=\Sigma_{n=1}^6 \dfrac{(-1)^{n+1}}{n^6} \approx 9.85545$
Hence, the sum of the series is $0.9856$ when approximated up to four decimals.