Statement I. The sum of the series is .
Statement II , for any natural number
Statement I is true, Statement II is true; Statement II is a correct explanation of Statement I
Explanation for the correct option:
Finding the sum of the series in statement I and solving the given expression in statement II:
On expanding the given polynomial by placing values of
Now solving for as the total number of digits in series are .
Substituting in the expression
[Using, ]
Therefore, Statement I and Statement II are true; and Statement II is a correct explanation of Statement I.
Therefore, the correct answer is option (B).