+0  
 
0
66
1
avatar

Compute 2018^2 - 2017^2 + 2016^2 - 2015^2 + ... + 4^2 - 3^2 + 2^2 - 1^2.

 May 24, 2020
 #1
avatar
0

Sum them up as an arithmetic sequence:

 

sum_(n=1)^1009((2020 - 2 n)^2 - (2019 - 2 n)^2) = 2,037,171

 

1009/2 * [2*4035 +  ( - 4*1008)] = S, solve for S

 

S =2,037, 171

 May 24, 2020

50 Online Users

avatar
avatar
avatar