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1 * P(first = 6) + 2 * P(second = 6) + ... 10 *P(first nine ! = 6)

= 1 * 1/6 + 2 * 5/6*1/6 + ... + 9 * (5/6)81/6 + 10*(5/6)9

The first 9 terms form an Arithemtico-geometric progression and we can find the sum using the formula given here:

https://en.wikipedia.org/wiki/Arithmetico-geometric_sequence

Or, we can sum them individually. Answer comes out to be 3.0928 and adding the last term gives 5.03

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