The real values of x for which y-1-2x-4x2-8x3-16x4- is finite-is-

The series 1+2x+4x^2+⋯ form GP with r=2x Si the sum becomes finite only if r lt;1 2 lt;x ...

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Proof by mathematical induction

The real valu...

Question

The real values of $x$ for which $y = 1 + \frac{2}{x} + \frac{4}{x^{2}} + \frac{8}{x^{3}} + \frac{16}{x^{4}} + . . . . . . \infty$ is finite,is:

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x_{1}, x_{2}, x_{3}, x_{4}, x_{5}

\sqrt{x_{1} - 1} + 2 \sqrt{x_{2} - 4} + 3 \sqrt{x_{3} - 9} + 4 \sqrt{x_{4} - 16} + 5 \sqrt{x_{5} - 25} = \frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5}}{2}

\frac{x_{1} + x_{2} + x_{3} + x_{4} + x_{5}}{2}

1 + \frac{2}{x} + \frac{4}{x^{2}} + \frac{8}{x^{3}} + . . . . (u p t o \infty), x \neq 0,

x

y

z_{1} = 9 y^{2} - 4 - 10 i x

x^{4} - x^{3} + x^{2} + 3 x - 5

x = 2 + 3 i

1 + \frac{2}{x}

\frac{4}{x^{2}}

\frac{8}{x^{3}}

\infty

1 + \frac{2}{x} + \frac{4}{x^{2}} + \frac{8}{x^{3}} + . . . . . . . . . t o \infty

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