Question

+1-2+3-4+5-6+......+101
Cum se rezolva?

Answer 1

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