Difference between revisions of "Sums"

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[[category: #sum of evens]]
 
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=== Find the last term ===
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{i=1}^{n} 2i=30</math><div class="mw-collapsible-content">
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[[comment: aₙ, 2, 30]]
 
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[[category: #sum of odds]]
 
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=== Find the last term ===
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<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{i=1}^{n} \left(2i-1\right)=36</math><div class="mw-collapsible-content">
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{{#annotask:
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[[category: #sum of odds]]
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[[comment: aₙ, 1, 36]]
 
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Revision as of 07:30, 8 January 2020

Sum of Natural Numbers

even number of terms = last term is even

[Expand]\scriptstyle\sum_{i=1}^8 i

[Expand]\scriptstyle\sum_{i=1}^{10} i

[Expand]\scriptstyle\sum_{i=5}^{10} i

[Expand]\scriptstyle\sum_{i=1}^{12} i

[Expand]\scriptstyle\sum_{i=1}^{18} i

[Expand]\scriptstyle\sum_{i=1}^{20} i

[Expand]\scriptstyle\sum_{i=1}^{100} i


odd number of terms = last term is odd

[Expand]\scriptstyle\sum_{i=1}^{7} i

[Expand]\scriptstyle\sum_{i=1}^{9} i

[Expand]\scriptstyle\sum_{i=1}^{11} i

[Expand]\scriptstyle\sum_{i=1}^{17} i

[Expand]\scriptstyle\sum_{i=1}^{19} i

Find the last term

[Expand]\scriptstyle\sum_{i=1}^{n} i=55

[Expand]\scriptstyle\sum_{i=1}^{n} i=465

Sum of Evens

[Expand]\scriptstyle\sum_{i=1}^{4} 2i

[Expand]\scriptstyle\sum_{i=1}^{5} 2i

[Expand]\scriptstyle\sum_{i=1}^{6} 2i

[Expand]\scriptstyle\sum_{i=3}^{6} 2i

[Expand]\scriptstyle\sum_{i=1}^{10} 2i

Find the last term

[Expand]\scriptstyle\sum_{i=1}^{n} 2i=30

Sum of Odds

[Expand]\scriptstyle\sum_{i=1}^{5} \left(2i-1\right)

[Expand]\scriptstyle\sum_{i=1}^{6} \left(2i-1\right)

[Expand]\scriptstyle\sum_{i=1}^{7} \left(2i-1\right)

[Expand]\scriptstyle\sum_{i=4}^{7} \left(2i-1\right)

[Expand]\scriptstyle\sum_{i=1}^{10} \left(2i-1\right)

Find the last term

[Expand]\scriptstyle\sum_{i=1}^{n} \left(2i-1\right)=36

Sum of Powers of Two = Sum of Even-Times-Even Numbers

[Expand]\scriptstyle\sum_{i=1}^{6} 2^{i-1}

[Expand]\scriptstyle\sum_{i=1}^{7} 2^{i-1}

[Expand]\scriptstyle\sum_{i=1}^{8} 2^{i-1}

[Expand]\scriptstyle\sum_{i=3}^{6} 2^{i-1}

Sum of Powers of Three

[Expand]\scriptstyle\sum_{i=1}^{4} 3^{i-1}

Sum of Powers of Four

[Expand]\scriptstyle\sum_{i=1}^{3} 4^{i-1}

Sum of Squares

[Expand]\scriptstyle\sum_{i=1}^{7} i^2

[Expand]\scriptstyle\sum_{i=1}^{12} i^2

Sum of Cubes

[Expand]\scriptstyle\sum_{i=1}^{5} i^3

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