Another form presents geometric sequence
If the real root of the equation above is of the form , where and are positive integers with minimized, find .
The answer is 4033.
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1 solution
k = 1 ∑ 2 0 1 6 x k = 1 − x x − 2 0 1 6
x − 1 x ( x 2 0 1 6 − 1 ) = 1 − x x − 2 0 1 6
x − 1 x 2 0 1 7 − x = x − 1 2 0 1 6 − x
x 2 0 1 7 − x = 2 0 1 6 − x
x 2 0 1 7 = 2 0 1 6
x = 2 0 1 7 2 0 1 6
⇒ a + b = 2 0 1 7 + 2 0 1 6 = 4 0 3 3