What digit is immediately on the right of the decimal point in ?

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- Aug 19th 2011, 04:59 PMalexmahoneWhat digit is immediately on the right of the decimal point?
What digit is immediately on the right of the decimal point in ?

- Aug 19th 2011, 06:11 PMSammySRe: What digit is immediately on the right of the decimal point?
What have you tried?

Where are you stuck? - Aug 19th 2011, 06:14 PMalexmahoneRe: What digit is immediately on the right of the decimal point?
- Aug 20th 2011, 01:09 AMmeleseIt looks right to me, but I may be wrong...
Write

*(*)*. Using the Binomial Theorem you can show that is an integer. (The terms with odd powers cancel each other, while those with even powers are integers.)

Let . As you've noted and therefore .

Rearranging*(*)*,we have*(^)*, meaning that is the**fractional part of**.

Since , it must start like this . So , by (^).