Răspuns:
Explicație pas cu pas:
( 5 + 10 + 15 + ...... + 2005 + 2010 ) : ( 1 + 2 + 3 + ..... + 401 + 402 ) = 5
= 5 × ( 1 + 2 + 3 + .... + 401 + 402 ) : ( 1 + 2 + 3 + ..... + 401 + 402 ) =
= 5
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Sau efectuand calculele, aplicand formula sumei lui Gauss
( 5 + 10 + 15 + ...... + 2005 + 2010 ) : ( 1 + 2 + 3 + ..... + 401 + 402 ) = 5
= 5 × ( 1 + 2 + 3 + .... + 401 + 402 ) : ( 1 + 2 + 3 + ..... + 401 + 402 ) =
= 5 × ( 402 × 403 : 2 ) : ( 402 × 403 : 2 ) =
= 5 × ( 201 × 403 ) : ( 201 × 403 ) =
= 5 × 81 003 : 81 003 =
= 5
