Răspuns:
Explicație pas cu pas:
+ 1 - 2 + 3 - 4 + 5 - 6 + ........ + 101 = 51
= ( 1 + 3 + 5 + 7 + ........ + 101 ) - ( 2 + 4 + 6 + ...... + 100 ) =
= [( 101 - 1 ) : 2 + 1 ] × ( 1 + 101 ) : 2 - 2 × ( 1 + 2 + 3 + ....... + 50 ) =
= ( 51 × 102 : 2 ) - 2 × ( 50 × 51 ) : 2 =
= 51 × 51 - 50 × 51 =
= 51 × ( 51 - 50 ) =
= 51 × 1 =
= 51
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1 + 3 + 5 + 7 + ........ + 101 =
→ deduc cati termeni are suma numerelor impare ( ratia = 2 )
( 101 - 1 ) : 2 + 1 = 100 : 2 + 1 = 51 termeni are suma numerelor impare ( prima paranteza )
→ aplic formula sumei lui Gauss
