Question : The 12th term of the series $\frac{1}{x}+\frac{x+1}{x}+\frac{2x+1}{x}+...$ is:
Option 1: $\frac{11x+1}{x}$
Option 2: $\frac{12x+1}{x}$
Option 3: $\frac{x+12}{x}$
Option 4: $\frac{x+11}{x}$
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Correct Answer: $\frac{11x+1}{x}$
Solution :
The given series is a sequence where each term is of the form $\frac{nx+1}{x}$, where n is the term number starting from 0.
So, the 12th term of the series (where n = 11 because we start from 0) would be
$\frac{11x+1}{x}$.
Hence, the correct answer is $\frac{11x+1}{x}$.
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