BUG/TST: PeriodArray.__setitem__ with slice and list-like value
- [ ] closes #23978 
- [ ] tests added / passed
- [ ] passes `git diff upstream/master -u -- "*.py" | flake8 --diff`
- [x] whatsnew entry

Hello @charlesdong1991! Thanks for submitting the PR.

 - There are no PEP8 issues in the file [`pandas/tests/arrays/test_period.py`](https://github.com/charlesdong1991/pandas/blob/43851287d1a0f1674c101c47d6b7d047c822e0fb/pandas/tests/arrays/test_period.py) !

 Great, your test has successfully raised the original bug: https://travis-ci.org/pandas-dev/pandas/jobs/461252693#L2863

So now you'll need to make the changes to `PeriodArray.__setitem__` to fix the bug. Make sense? thank you very much @TomAugspurger ! this time it should work!  Some linting failures

https://travis-ci.org/pandas-dev/pandas/jobs/461404542#L2851

https://travis-ci.org/pandas-dev/pandas/jobs/461404542#L2868 HI, @TomAugspurger , ehh, this Flaky error appears again... Is it because my changes didn't pass the hinting test? # [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=h1) Report
> Merging [#23991](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=desc) into [master](https://codecov.io/gh/pandas-dev/pandas/commit/43b2dabdcab50e0c83e37b0b8debcd579c539a9f?src=pr&el=desc) will **decrease** coverage by `49.86%`.
> The diff coverage is `0%`.

[![Impacted file tree graph](https://codecov.io/gh/pandas-dev/pandas/pull/23991/graphs/tree.svg?width=650&token=eZ4WkYLtcO&height=150&src=pr)](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=tree)

```diff
@@             Coverage Diff             @@
##           master   #23991       +/-   ##
===========================================
- Coverage   92.31%   42.44%   -49.87%     
===========================================
  Files         161      161               
  Lines       51513    51562       +49     
===========================================
- Hits        47554    21888    -25666     
- Misses       3959    29674    +25715
```

| Flag | Coverage Δ | |
|---|---|---|
| #multiple | `?` | |
| #single | `42.44% <0%> (+0.02%)` | :arrow_up: |

| [Impacted Files](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=tree) | Coverage Δ | |
|---|---|---|
| [pandas/core/arrays/period.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvYXJyYXlzL3BlcmlvZC5weQ==) | `37.02% <0%> (-61.42%)` | :arrow_down: |
| [pandas/io/formats/latex.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvbGF0ZXgucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/core/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvY2F0ZWdvcmljYWwucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/sas/sas\_constants.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfY29uc3RhbnRzLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/plotting.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvcGxvdHRpbmcucHk=) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/tseries/converter.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL3RzZXJpZXMvY29udmVydGVyLnB5) | `0% <0%> (-100%)` | :arrow_down: |
| [pandas/io/formats/html.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL2Zvcm1hdHMvaHRtbC5weQ==) | `0% <0%> (-97.64%)` | :arrow_down: |
| [pandas/core/groupby/categorical.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2NvcmUvZ3JvdXBieS9jYXRlZ29yaWNhbC5weQ==) | `0% <0%> (-95.46%)` | :arrow_down: |
| [pandas/io/sas/sas7bdat.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXM3YmRhdC5weQ==) | `0% <0%> (-91.17%)` | :arrow_down: |
| [pandas/io/sas/sas\_xport.py](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree#diff-cGFuZGFzL2lvL3Nhcy9zYXNfeHBvcnQucHk=) | `0% <0%> (-90.24%)` | :arrow_down: |
| ... and [120 more](https://codecov.io/gh/pandas-dev/pandas/pull/23991/diff?src=pr&el=tree-more) | |

------

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> `Δ = absolute <relative> (impact)`, `ø = not affected`, `? = missing data`
> Powered by [Codecov](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=footer). Last update [43b2dab...6c9702e](https://codecov.io/gh/pandas-dev/pandas/pull/23991?src=pr&el=lastupdated). Read the [comment docs](https://docs.codecov.io/docs/pull-request-comments).
 thanks @charlesdong1991 