Hi Yoko, There is no reason why you cannot use the gerund (-ing form) after 'such as' and 'like'. In fact, I prefer it to the infinitive, since we are speaking of 'jobs'. 'Such as' and 'like' are both used to preface examples, but 'such as' is more formal than 'like'.
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Hello. It may be helpful to understand the word 'like' a little more then once you have grasped this is may be easier to know when to use 'like' and when to use 'such as'. This short blog post 10 common uses of the word like may be useful for you!