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Expected value of highest dice rolled

You roll N dice simultaneously. Your score is the highest number rolled. If you play this game many times, what is the expected value (mean) of your score?

## Input
- A positive integer.
- Your code must work for inputs up to and including 10, but may crash or error for larger inputs.

## Output
- The expected value (the mean value) of the dice result which is highest when N dice are rolled simultaneously.
- For inputs up to and including 10, the output must be correct to 6 decimal places.
- If you provide more than 6 decimal places, they do not need to be correct.

## Test cases
- Test cases are in the format `input : output`.
- Outputs are shown to 29 decimal places, but only the first 6 are required.
- Inputs are listed up to 100, but only the first 10 are required.

```text
1 : 3.50000000000000000000000000000
2 : 4.47222222222222222222222222222
3 : 4.95833333333333333333333333333
4 : 5.24459876543209876543209876543
5 : 5.43094135802469135802469135802
6 : 5.56029235253772290809327846365
7 : 5.65411736968449931412894375857
8 : 5.72435425716354214296601127877
9 : 5.77817697616598079561042524005
10 : 5.82015937306834154685092042202
11 : 5.85335706527894206506460735999
12 : 5.87988997582530915943632501068
13 : 5.90127519231210814088487715475
14 : 5.91862670254239982137663865269
15 : 5.93278028294863316396677461217
16 : 5.94437438620726706763129530818
17 : 5.95390415952465750681465958813
18 : 5.96175850647834296160754452251
19 : 5.96824613483573478052351165790
20 : 5.97361426407447557663984765006
21 : 5.97806232620687085074595293012
22 : 5.98175217846144708662154353022
23 : 5.98481583773702261975593217245
24 : 5.98736142198727564742707212114
25 : 5.98947777205805890939664416722
26 : 5.99123808700442039912763192534
27 : 5.99270281104071658824509961829
28 : 5.99392194517515569233729905843
29 : 5.99493691121505910010725938052
30 : 5.99578206374053429687749343718
31 : 5.99648592261006367516482569756
32 : 5.99707218178527995084736694167
33 : 5.99756053786868087649928650274
34 : 5.99796737246493066079858958712
35 : 5.99830631543055017861569950830
36 : 5.99858871066207446521322300997
37 : 5.99882400186341138245450681838
38 : 5.99902005242648948549576095711
39 : 5.99918341093743479553132394038
40 : 5.99931953172456703574223466691
41 : 5.99943295817706350108795983587
42 : 5.99952747519634081538911322617
43 : 5.99960623602945068095518442501
44 : 5.99967186782397404767755480207
45 : 5.99972655949737104393862636712
46 : 5.99977213489940115923030314943
47 : 5.99981011373944957989563752749
48 : 5.99984176233172849189022933653
49 : 5.99986813586456479870290813229
50 : 5.99989011361255339407569498867
51 : 5.99990842827184954870321285747
52 : 5.99992369040080016589174296589
53 : 5.99993640878350603044198445896
54 : 5.99994700739703671894286363020
55 : 5.99995583954916283311195393381
56 : 5.99996319965872384717127603489
57 : 5.99996933307188419526385210950
58 : 5.99997444424186859925185882190
59 : 5.99997870354508945667904295502
60 : 5.99998225296104051857478470078
61 : 5.99998521080539996849966854970
62 : 5.99998767567418855349310233867
63 : 5.99998972973050506993796648767
64 : 5.99999144144343063073206840811
65 : 5.99999286787042090723765344027
66 : 5.99999405655928101044676381654
67 : 5.99999504713313212275883242164
68 : 5.99999587261120873388929359398
69 : 5.99999656050951747707865703098
70 : 5.99999713375804914123485643137
71 : 5.99999761146511955791960329286
72 : 5.99999800955431870285999319781
73 : 5.99999834129530052211240888309
74 : 5.99999861774610705935749422818
75 : 5.99999884812177141008489719171
76 : 5.99999904010148652659540160860
77 : 5.99999920008457900651260250252
78 : 5.99999933340382043943812434706
79 : 5.99999944450318676665018476267
80 : 5.99999953708599101695409676737
81 : 5.99999961423832721062548685767
82 : 5.99999967853194025096373203645
83 : 5.99999973210995081498699422189
84 : 5.99999977675829274972286241220
85 : 5.99999981396524422736929682262
86 : 5.99999984497103703565235500206
87 : 5.99999987080919764938447871130
88 : 5.99999989234099812093652084287
89 : 5.99999991028416515396895975767
90 : 5.99999992523680433043315027918
91 : 5.99999993769733696566696999774
92 : 5.99999994808111415381537150814
93 : 5.99999995673426180535251837455
94 : 5.99999996394521817813134894619
95 : 5.99999996995434848644562432230
96 : 5.99999997496195707515102040223
97 : 5.99999997913496423136785042429
98 : 5.99999998261247019419009763519
99 : 5.99999998551039182941411843930
100 : 5.99999998792532652512667897273
```

## Scoring
This is a [code golf challenge]. Your score is the number of bytes in your code.

> Explanations are optional, but I'm more likely to upvote answers that have one.



[code golf challenge]: https://codegolf.codidact.com/categories/49/tags/4274 "The code-golf tag"