Help with sum of notation

Question

Can you ever represent series in sigma notation?

can the series 1+4+9+61+52 be represented in sigma notation

Answer 1

First, ask yourself the question, “Can I express all the terms as functions of i; where i represents the position of the term in the series?”

Yes – the terms are the digits of the squares of the position, only reversed.  For example, series term 5 is 5*5=25 reversed, which is 52.

 

Sigma notation has a starting point and an ending point for the index, often the variable i.  In this problem, i ranges from 1 to 5. Now, we need to separate digits – the unit’s digit and the power-of-ten’s digit.  We can use the Mod (the remainder function) for that.  For example, Mod(25,10)=5 and (25-Mod(25,10))/10=2.  Now, to give the units digit a tens’ value, multiply it by 10.

 

And, to represent the sum (in Sigma) notation:

            5

            ∑ [ 10*Mod(i²,10) + ( i²-Mod(i²,10) )/10 ]
          i=1
 

Answer 2

Hi,

 

It is impossible to express the given series in sigma notation because your given pattern is made by reversing the digits of squared numbers and it can be interpreted in several ways.

 

1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169...

 

1, 4, 9, 61, 52, 63, 94, 46, 18, 1, 121, 441, 961...

 

As Shradha said, you can represent it in sigma form if the pattern looks like sum of squared numbers.

 

Gaurav

Answer 3

this seems like series of squres of natural numbers .....1+4+9+16+25  ......0r   1²+2²+3²+4²+5^2....

 

 

or   ∑ n²     ; where n= 1,2,3,4,5...

     

                                                                                                                                  
if last term is 25 then series will be finite and then it will be represented as

 

5

∑ n²

n=1