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Algebra Level 2

1 + a + a 2 + a 3 + . . . + a x − 1 + a x = ( 1 + a ) ( 1 + a 2 ) ( 1 + a 4 ) ( 1 + a 8 ) 1+a+a^2+a^3+...+a^{x-1}+a^x=(1+a)(1+a^2)(1+a^4)(1+a^8) .

x 15 = ? \frac{x}{15}=?


The answer is 1.

John M. by John M. , 24, USA

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2 solutions

U Z
Sep 24, 2014

multiply both the sides by ( 1- a) thus we get 1 − a x + 1 = 1 − a 16 1 -a^{x+1} = 1 - a^{16} thus x=15

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Lee Hang Zheng
Sep 7, 2014

From the series we can tell x is the highest obtainable power for a. From the differentiated equation, we know the greatest power of a is 1+2+4+8=15 Hence, x=15 when divided by 15 equals to 1.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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