I think something is missing especially the defintion of the the sequence, check it out please~

Sorry about that!
Fixed..
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Explanation

Decoding the definition of the sequence tells you that, to find the value of each term, you take the previous term, and raise it to the power of the term before it. You know

\(S_{3}=10^2=100\) and \(S_{4}=100^{10}=10^{20}\) and \(S_{5}=(10^{20})^{100}=10^{2000}\).

So \(S_{4}\) is the digit 1 followed by twenty zeroes, which is a total of 21 digits, and \(S_{5}\) is the digit 1 followed by 2,000 zeroes, for a total of 2,001 digits. So the fourth term is the one that meets the condition set forth in the question, and the answer is choice (D).
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