a ) S = 20 +22 + 24 +...+ 22014
4S = 22 + 24 + 26 + ... + 22016
Mà S = ( 4S- S ) : 3
=> S = [ ( 22 + 24 + 26 +...+ 22016 ) - ( 20 + 22 + 24 +...+ 22014 ) ] : 3
= [ 22016 - 20 ] : 3
= \(\frac{2^{2016}-1}{3}\)
b) S = 20 + 22 + 24 + ... + 22014
= ( 20 + 22 + 24 ) + ( 25 + 26 + 27 ) + ...+ ( 22010 + 22012 + 22014 )
= 21 + 25 x ( 20 + 22 + 24 ) +... + 22010 x ( 20 + 22 + 24 )
= 21 + 25 x 21 + ... + 22010 x 21
= 21 x ( 1 + 25 + ... + 22010 )
=> S \(⋮\)21 (đpcm)
Đúng 0
Bình luận (0)
