Number 46

I found the first 7 terms to be .78343057

Since I want to 7 places I added the value when n=8 (5.96x10^-8) to my initial value

So .78343057<f(x)<.78343051

So I claim that the sum of the series should be .7834305

My teacher told me this is wrong but could not explain why. His value was .783431

Where is my mistake?

Listing from phone so hard to type out step by step at the moment.