For the series below calculate the sum of the first 3 terms, S3\displaystyle {S}_{{3}}, and find a bound for the error. Make sure to include at least several decimals for accuracy when the problem is graded.

n=1((1)n200n0.8)\displaystyle {\sum_{{{n}={1}}}^{\infty}}{\left({\frac{{{\left(-{1}\right)}^{{n}}{200}}}{{{n}^{{0.8}}}}}\right)}


S3=\displaystyle {S}_{{3}}=  

|error| \displaystyle \le