Four verbs in English, which can be followed by either Gerund (doing) or Infinitive (to do), (not followed by object) without any difference in meaning include: ‘begin, start, continue and cease’ when you use Present Simple and other Simple Tenses. ( Past Simple, Present Perfect Simple, Past Perfect Simple, Future Simple and Future Perfect Simple)
You can say:
‘I always begin studying before my exams’ or ‘I always begin to study before my exams’, it means the same. (Present Simple)
‘I started swimming in July’ or ‘I started to swim in July’, it means the same. (Past Simple)
‘She has continued to travel in Europe” or ‘She has continued traveling in Europe ” it means the same. (Present Perfect Simple)
The verb to ‘cease’ is often (not always) more formal. You can say:
‘ Without proper funding the university will cease to exist’ or ‘Without proper funding the university will cease existing’ it means the same (Future Simple)
EXCEPTIONS:
However, if you use Continuous Tenses, with ‘begin’ or “start” only infinitive can be used:
‘I’m beginning to understand ” (Present Continuous)
‘I was starting to believe’ (Past Continuous)
(You cannot say; ‘I’m beginning understanding’ or ‘I was starting believing’. It is incorrect)
LAST EXCEPTION:
The verb: ‘to cease” is not used with Continuous Tenses.
That’s it. Hope this helps! 
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Greg