SOLUTION: 2c. Examine the diagram and explain how it illustrates a value of (n2 + n)/2. ⚫⚫⚫🔴 ⚫⚫🔴🔴

Algebra ->  Sequences-and-series -> SOLUTION: 2c. Examine the diagram and explain how it illustrates a value of (n2 + n)/2. ⚫⚫⚫🔴 ⚫⚫🔴🔴       Log On


   

Question 1144206: 2c. Examine the diagram and explain how it illustrates a value of (n2 + n)/2.
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2d. Draw a similar diagram to represent +%28n%5E2+%2B+n%29%2F2+ for n = 5.
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


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That diagram illustrates (n^2+n)/2 for n=3.

For n=3, n^2+n = n(n+1) = 3(4); the diagram shows a 3x4 array of circles. Dividing the array in half diagonally illustrates (n^2+n)/2 for n=3:

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This array then shows that (n^2+n)/2 for n=3 is equal to 1+2+3 = 6.

For n=5, (n^2+n)/2 = (n(n+1))/2 = (5*6)/2, so the corresponding diagram will show a 5x6 array of circles divided in half diagonally:

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And this diagram shows that (n^2+n)/2 for n=5 is equal to 1+2+3+4+5 = 15.