Do you know its property? (4)

Algebra Level 5

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

Details and Assumptions:

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

  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 \(\binom{n}{r}=0\) if \(n<r\).


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