Skipping sums

Algebra Level 3

If \(a + a^2 + a^3 + a^4 + a^5 + \cdots \) is a positive number, then which of the following is larger,

\[a+a^3+a^5+a^7+\cdots\quad \text{or}\quad a^2+a^4+a^6+a^8+\cdots\, ?\]

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