Question

Sa se calculeze: $^{n}$
S= Σ 3k+1
$_{k=1}$

Answer 1

= ( 3 ·1 + 1 ) + (3·2  + 1) + .. + ( 3·n + 1) 
 = 3 · ( 1 +2+ .. + n )  + 1 · n = 
= 3 · ( n +1 ) · n / 2    + n = 
 = n · [ 3·( n +1 ) / 2  + 1 ] = = n · ( 3·n + 3 + 2 ) / 2 = n· ( 3·n + 5 ) /2