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an = 2^n + 2^(n+1) + ... + 2^(2n-1)
= 2^n * ( 1 - 2^n )/ (1 - 2 ) = 2^n * ( 2^n - 1 ) = 4^n - 2^n
bn = (-1)^n * n^2 + n
S100 = [ ( -1^2 + 2^2 ) + ( -3^2 + 4^2 ) + ... + ( -99^2 + 100^2 ) ] + ( 1 + 2 + 3 + ... + 100 )
= [ ( 1 + 2 ) + ( 3 + 4 ) + ... + ( 99 + 100 ) ] + ( 1 + 2 + 3 + ... + 100 )
= 2 * ( 1 + 2 + 3 + ... + 100 )
= ( 1 + 100 ) * 100
= 10100
= 2^n * ( 1 - 2^n )/ (1 - 2 ) = 2^n * ( 2^n - 1 ) = 4^n - 2^n
bn = (-1)^n * n^2 + n
S100 = [ ( -1^2 + 2^2 ) + ( -3^2 + 4^2 ) + ... + ( -99^2 + 100^2 ) ] + ( 1 + 2 + 3 + ... + 100 )
= [ ( 1 + 2 ) + ( 3 + 4 ) + ... + ( 99 + 100 ) ] + ( 1 + 2 + 3 + ... + 100 )
= 2 * ( 1 + 2 + 3 + ... + 100 )
= ( 1 + 100 ) * 100
= 10100
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