# Math Help - Mathematical Induction

1. ## Mathematical Induction

Prove using mathematical induction:

49|(2^(3n) - 7n - 1)

2. Originally Posted by MATNTRNG
Prove using mathematical induction:

49|(2^(3n) - 7n - 1)

Check for n = 1 and complete the explanation in the following:

$2^{3(n+1)}-7(n+1)-1=8\cdot 2^{3n}-7n-7-1=\left(2^{3n}-7n-1\right)+7\cdot 2^{3n}-7=$ $49k+7\left(2^{3n}-1\right)=49k+7(2^3-1)(2^{3(n-1)}+2^{3(n-2)}+\ldots+2^3+1)$ , $k\in\mathbb{N}$

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