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Can you add a half plus a third plus a quarter continuing to infinity?
Wiki User
∙ 14y ago
1/2 + 1/3 + 1/4 + ... + 1/∞ = ∞
(1/2 + 1/3) > 1
(1/4 + 1/5 + 1/6 + 1/7 + 1/8 + 1/9 + 1/10) > 1
(1/11 + 1/12 + 1/13 + 1/14 + 1/15 + 1/16 + 1/17 + 1/18 + 1/19 + 1/20 + 1/21 + 1/22 + 1/23 + 1/24+ 1/25 + 1/26 + 1/27 + 1/28 + 1/29) > 1
The number of terms necessary to comprise an additional 1 increase slowly, the sum continues towards infinity.
As there are an infinite number of terms, the series will indeed sum to ∞, and, as a result, is divergent.
Wiki User
∙ 14y ago
Jim Botaitis
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3
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