Do if you can
If x is a rational number such that
( 1 − x ) ( 1 + x + x 2 + x 3 + x 4 ) = 3 1 / 3 2 ,
then find the value of
1 + x + x 2 + x 3 + x 4 + x 5 .
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1 solution
It's better to state that ( 1 − x ) ( 1 + x + x 2 + … + x n ) = 1 − x n + 1 .
And explain why x = 2 1 is the only solution for x 5 = 3 2 1 .
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Because x is a real rational number.
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That doesn't explain why it's the only solution.
Then sir, please explain why , i want to know please.
please remove the 'apparent' negative sign from the front of the equation
it is highly confusing
By sum of n terms of GP: a(1-r^n)/(1-r) (1-x)*1(1-x^5)/(1-x)= 31/32 1-x^5=31/32 x^5=1/32 x=1/2
1+x+x^2+x^3+x^4+x^5=1{1-(1/2)^6} =(63/64)/(1/2) =63*2/64 =63/32