Let $T(n) = T(n-1) + \frac{1}{n} , T(1) = 1 ;$ then $T(n) = ? $
If we use H.P. sum formula it will come as log(something). So by intuitively we can say option B is correct
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this is the way to dealing with such type of question
Ok, your method is good, but
How you take the condition
where $n>1$ given in the question, you take $k =n-1$,right??
if $n>=1$ given the question, what we take $k =?$
if $n>=0$ given the question, what we take $k =?$
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