m: sum:
1 64.4934066848226436472415166646025189218949901206798437735
2 72.7257300559364627988418863187193091993700853125525345418
3 74.4600362543813767702936792978113619895518343158378907260
4 74.8677718741758107081622031486766085154479133808228927590
5 74.9672293869576192418767990387085102160498665372706444847
6 74.9918380422884240717405988434824773120914753830709849380
7 74.9979628557942945546664533539960106868396449999864398863
8 74.9994910817351597418397105027596828891633838990335930016
9 74.9998728110616597258253566672218768622088536209289261159
10 74.9999682072650470054366718710902217968032330396699856909
11 74.9999920523153197787356722359088970962967372218479515179
12 74.9999980131342249046836334799296906764194876137316817975
13 74.9999995032897077411877569457803537462823740925484703886
14 74.9999998758231102200334624277007555865246973818543999697
15 74.9999999689558534620002807148772290886466787386499136513
16 74.9999999922389717987653356348917888480516289869481421044
17 74.9999999980597438866680365241354748371579344042604025661
18 74.9999999995149360757722349477284380616897765026412919785
19 74.9999999998787340305101000667521616972771038539058948170
20 74.9999999999696835089127389595774928811465947292918949161
By approximation from this online regression tool I've been able to generate: $$y=74.75560361 + \frac{4.829026118}{x} - \frac{19.87124992}{x^2} + \frac{4.776049777}{x^3}$$
This is important because it would provide a "more reasonable" object on which to perform calculus and elementary algebra on. It would also save quite a bit of time computationally. I am aware of the limit as $m$ goes to infinity, that's just the infinite sum. I am looking for something that calculates the partial sum well.