+0  
 
+1
187
5
avatar+27 

Find the value of series

\[1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + \cdots + 24 + 96 + 25 + 100.\]

 

Thank you!!

 May 17, 2022
edited by IcanhelpandIneedhelp  May 17, 2022
 #1
avatar
0

Using arithmetic series, the sum is 1750.

 May 17, 2022
 #2
avatar+27 
+1

Pls do not lie and the answer is incorrect.

 May 17, 2022
 #3
avatar+2448 
0

Consider it as 2 seperate series: \(1 + 2 + 3 + 4 + \cdot \cdot \cdot+ 24 +25\)and \(4+8+12+16 + \cdot \cdot \cdot + 96+100\)

 

The sum of the first series is simple, as the sum can be defined as: \(25 \times 26 \div 2 = 325\)

 

To make things easier, we can express the second series in multiples of 4 as follows: \(1(4) + 2(4) + 3(4) + 4(4) + \cdot \cdot \cdot + 24(4) + 25(4)\)

 

This can be rewritten as: \((1 + 2 +3+4\cdot \cdot \cdot +24 +25)\times 4 \). Thus, the sum of the second series is: \(325 \times 4 = 1300\)

 

Can you find the answer from here?

 May 17, 2022
 #4
avatar+26330 
+4

Find the value of series
\(1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + \cdots + 24 + 96 + 25 + 100.\)

 

\(\begin{array}{|rcll|} \hline 1+4 &=& 5 \\ 2+8 &=& 10 \\ 3+12 &=& 15 \\ 4+16 &=& 20 \\ \ldots \\ 24 + 96 &=& 120 \\ 25 + 100 &=& 125 \\ \hline \end{array}\)

 

\(\begin{array}{|rcll|} \hline && 1 + 4 + 2 + 8 + 3 + 12 + 4 + 16 + \cdots + 24 + 96 + 25 + 100\\ &=& 5+10+15+20 + \cdots +120+125 \\ &=& 5*(1+2+3+4+\cdots +24+25) \\ && \boxed{ 1+2+3+4+\cdots +24+25 = \frac{1+25}{2}*25 \\ =13*25 \\ = 325 } \\ &=& 5*325 \\ &=& \mathbf{1625} \\ \hline \end{array}\)

 

laugh

 May 18, 2022
edited by heureka  May 18, 2022
 #5
avatar+118146 
0

Hi Heureka,

It is really nice to see you here again :)

Melody  May 18, 2022

19 Online Users