DOC: Add whatsnew entry for pandas-dev#61099

Author: MayurKishorKumar

doc/source/whatsnew/v3.0.0.rst

@@ -706,6 +706,7 @@ Indexing
 - Bug in :meth:`MultiIndex.insert` when a new value inserted to a datetime-like level gets cast to ``NaT`` and fails indexing (:issue:`60388`)
 - Bug in printing :attr:`Index.names` and :attr:`MultiIndex.levels` would not escape single quotes (:issue:`60190`)
 - Bug in reindexing of :class:`DataFrame` with :class:`PeriodDtype` columns in case of consolidated block (:issue:`60980`, :issue:`60273`)
+- Bug in :meth:`Series.equals` and :meth:`Series.__eq__` where equality comparison would fail if the index values were equal but had differing dtypes (e.g. ``object`` vs ``string``). (:issue:`61099`)
 
 Missing
 ^^^^^^^