Power ^ ... ^ ...

What is the next numbers in this series.

2, 11, 75, 700, 8476, ... ?,


The answer is 126125.

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2 solutions

It is of the general form a n = a n 1 + ( n + 1 ) n a_n = a_{n-1} + (n+1)^{n}

Therefore a 6 = a 5 + 7 6 a_6 = a_5 + 7^6 a 6 = 8476 + 117649 a_6 =8476 + 117649 126125 \boxed {126125}

Ossama Ismail
Apr 17, 2015

The next number in the series is 126125. The pattern is -

2 = 2^1

11 = 2^1 + 3^2

75 = 2^1 + 3^2 + 4^3

700 = 2^1 + 3^2 + 4^3 + 5^4

8476 = 2^1 + 3^2 + 4^3 + 5^4 + 6^5

126125 = 2^1 + 3^2 + 4^3 + 5^4 + 6^5 + 7^6

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