Why Is the Sum of 1/2 (n+1)/2?

Thread starter theintarnets
Start date Jun 3, 2013
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Sum

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The summation of 1/2 from i=0 to n results in (n+1)/2 because the index starts at zero, leading to n+1 total terms. Each term contributes 1/2, so the total is (n+1) times 1/2. This clarifies why the answer is not simply n/2, which would imply only n terms. Understanding the impact of the starting index is crucial in evaluating summations. The key takeaway is that the inclusion of the zero index adds an additional term to the total count.

Jun 3, 2013

theintarnets

I don't understand why the answer to this summation:
_n
Ʃ 1/2
^{i = 0}

is (n+1)/2
Why isn't it just n/2?

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Jun 3, 2013

LCKurtz

Science Advisor

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theintarnets said:

I don't understand why the answer to this summation:
_n
Ʃ 1/2
^{i = 0}

is (n+1)/2
Why isn't it just n/2?

Because the index starts at zero. 0,1,2,...n has n+1 terms.

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