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avatar+109 

Can someone please explain to me how to solve a summation with subscripts.

 May 21, 2014

Best Answer 

 #3
avatar+33615 
+10

This just means add up the individual terms (and divide the result by n).  For example 

$$If the $X$'s were $X_1,X_2,X_3$ then $\sum_{k=1}^3X_k = X_1+X_2+X_3$\\\\
Sometimes you might have a function to sum, rather than a set of data; and sometimes that summation might simplify. For example\\
$$\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}{6}$$

 I should perhaps expand that last one a little:

$$$$\sum_{k=1}^nk^2=1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$$

 May 22, 2014
 #1
avatar+128408 
+5

Could you provide an example of what you want to do??

 May 21, 2014
 #2
avatar+109 
0

Let's take the Law of Large Numbers for instance:

 

\overline{X}_n=\frac1n{\sum_{k=1}^n X_k}

 May 21, 2014
 #3
avatar+33615 
+10
Best Answer

This just means add up the individual terms (and divide the result by n).  For example 

$$If the $X$'s were $X_1,X_2,X_3$ then $\sum_{k=1}^3X_k = X_1+X_2+X_3$\\\\
Sometimes you might have a function to sum, rather than a set of data; and sometimes that summation might simplify. For example\\
$$\sum_{k=1}^nk^2=\frac{n(n+1)(2n+1)}{6}$$

 I should perhaps expand that last one a little:

$$$$\sum_{k=1}^nk^2=1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$$

Alan May 22, 2014

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