Difference between revisions of "Sums"

From mispar
Jump to: navigation, search
(→‎Sum of Natural Numbers)
(→‎Sum of Odds)
Line 128: Line 128:
 
}}</div></div><br>
 
}}</div></div><br>
  
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{i=4}^{7} \left(2i-1\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #sum of odds]]
 +
[[comment: 7-13]]
 +
}}</div></div><br>
 +
 +
<div class="mw-collapsible mw-collapsed"><math>\scriptstyle\sum_{i=1}^{10} \left(2i-1\right)</math><div class="mw-collapsible-content">
 +
{{#annotask:
 +
[[category: #sum of odds]]
 +
[[comment: 1-19]]
 +
}}</div></div><br>
  
 
== Sum of Powers of Two = Sum of Even-Times-Even Numbers ==
 
== Sum of Powers of Two = Sum of Even-Times-Even Numbers ==

Revision as of 20:15, 7 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=465

Sum of Evens

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

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

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

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)

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

Retrieved from "http://mispar.ethz.ch/mediawiki/index.php?title=Sums&oldid=41535"