Find the value of t without using caculator

Algebra Level 4

t = 1 n + 2 n + 3 n + + 1 0 n + 1 1 n \large t = 1^n + 2^n + 3^n + \cdots +10^n + 11^n

If n n is an integer and 381500 < t < 382000 381500 < t < 382000 , what is the value of t t ?


The answer is 381876.

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