Calculate the first eight terms of the sequence of partial sums correct to four decimal places. 1/n⁴ + n².

Solution:

The objective of the problem is to find out the sum of the first 8 terms of the expression (1/n⁴ + n².).

Such an action can be summarised as follows:

\( \sum_{1}^{8}(\frac{1}{n^{4}} + n^{2}) \)

= \( [(\frac{1}{1^{4}})+ 1^{2}] + [\frac{1}{2^{4}}+ 2^{2}] + [\frac{1}{3^{4}}+ 3^{2}] + [\frac{1}{4^{4}}+ 4^{2}] + [\frac{1}{5^{4}}+ 5^{2}] + [\frac{1}{6^{4}}+ 6^{2}] + [\frac{1}{7^{4}}+ 7^{2}] + [\frac{1}{8^{4}}+ 8^{2}] \)

= 2 + 4.0625 + 9.0123 + 16.0039 + 25.0016 + 36.0007 + 49.0004 + 64.0004

= 205.0818 Answer