+0  
 
0
58
1
avatar

In the sequence 1,4,4,9,9,9,16,16,16,16, ... Find the sum of first 99 terms.

 Jun 16, 2020
 #1
avatar+25532 
+1

In the sequence \(1,\ 4,\ 4,\ 9,\ 9,\ 9,\ 16,\ 16,\ 16,\ 16, \ \ldots\)
Find the sum of first 99 terms.

 

\(\begin{array}{|rcll|} \hline && 1,\ 4,\ 4,\ 9,\ 9,\ 9,\ 16,\ 16,\ 16,\ 16, \ \ldots ,\ 169,\ 196,\ 196,\ 196,\ 196,\ 196,\ 196,\ 196,\ 196 \\ s &=& 1*1^2+2*2^2+3*3^2+4*4^2+5*5^2+6*6^2+ \ldots + 13*13^2 + 8*14^2 \\ s &=& 1^3+2^3+3^3+4^3+5^3+6^3+7^3+8^3+9^3+10^3+11^3+12^3+ 13^3 + 8*14^2 \\ s &=& \left(\dfrac{13*(13+1)}{2}\right)^2+ 8*14^2 \\ s &=& \left(\dfrac{13*14}{2}\right)^2+1568 \\ s &=& (13*7)^2+1568 \\ s &=& 91^2+1568 \\ s &=& 8281+1568 \\ \mathbf{s} &=& \mathbf{9849} \\ \hline \end{array}\)

 

laugh

 Jun 16, 2020

18 Online Users

avatar
avatar