Read the following instruction carefully and answer the question that follows:
Expression
∑n=1131n can also be written as x13!
What would be the remainder if x is divided by 11?
Explanation:
∑n=1131n=x13!∴x=13!1+13!2+13!3+...+13!11+13!12+13!13
All the terms in x are divisible by 11 except 13!/11
13!11=1.2.3.4...10.12.13
According to Wilson theorem,
rem(p-1)!p=-1
13!11=1.2.3.4...10.12.13.=10!(12)(13)
∴rem 13!1111=10!(12)(13)11=(-1).1.2=-2=9
Hence, option (d).
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