Series

We can split this into  two series

2 + 8 + 32 +  128  + 512      and     -1 + -4 + - 16 + - 64 + -256  = - [ 1 + 4 + 16 + 64+ 256 ]

Note that the first series can be written as

2 [ 1 + 4 + 16 + 64+ 256 ] 

So the sum of the two series  is

2 [A]  - [A]       =   A   

Where A  is just  1 + 4 + 16 + 64+ 256   =  341 !!!

Sum =F x [1 - R^N] / [1 - R], where F=First term, R=Common ratio, N=Number of terms

Sum =-1 x [1 - (-2^10] / [1 - (-2)]

Sum =-1 x [1 - 1,024] / [3]

Sum =-1 x[ -1023] / 3

Sum = 1,023/3

Sum = 341