Do you know its property? (4)

Algebra Level 5

If tn=8+6(n11)+2(n12)t_{n}=8+ 6\binom{n-1}{1}+2\binom{n-1}{2}, then find the digit sum of n=11729(tn).\displaystyle \large\sum_{n=1}^{1729} (t_{n}).

Details and Assumptions:

  1. (nr)=n!r!×(nr)!\binom{n}{r}=\dfrac{n!}{r! \times (n-r)!}.

  2. Digit sum refers to the sum of the digits of the number. For instance, Digit sum of 1729 is 1+7+2+9=19.

  3. Assume (nr)=0\binom{n}{r}=0 if n<rn<r.

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