Question

dau coroana pls pana la 16:00

Answer 1

( 4 + 8 + 12 + ......+ 2 012 ) : ( 2 + 4 + 6 + ........+ 1 006) = 2

→ il dau factor comun pe 2

= 2 × ( 2 + 4 + 6 + ........+ 1 006 ) : ( 2 + 4 + 6 + ....+ 1 006 ) =

= 2

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6 + 11 + 16 + 21 + .......+ 506 =

r = 5

→ stabilim cati termeni are suma: ( 506 - 6 ) : 5 + 1 = 500 : 5 + 1 = 101 termeni

= 101 × ( 6 + 506 ) / 2 = 101 × 512 / 2 = 101 × 256 = 25 856

sau descompun :

6 + ( 6 + 5 ) + ( 6 + 10 ) + ( 6 + 15 ) + ......+ ( 6 + 500) =

= 6 × 101 ( termeni) + 5 × ( 1 + 2 + 3 + ..........+ 100 ) =

= 606 + 5 × ( 100 × 101 / 2 ) =

= 606 + 5 × 50 × 101 =

= 606 + 25 250 =

= 25 856

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4 + 9 + 14 + 19 + ......+ 1 004 =

r = 9 - 4 = 5

→ stabilim cati termeni are suma

( 1 004 - 4 ) : 5 + 1 = 1 000 : 5 + 1 = 201 termeni are suma

→ aplic formula sumei lui Gauss

= 201 × ( 1004 + 4 ) / 2 = 201 × 504 = 101 304

sau prin descompunere:

= 4 + ( 4 + 5 ) + ( 4 + 10 ) + ( 4 + 15 ) + .......+ ( 4 + 1 000 ) =

= 4 × 201 + 5 × ( 1 + 2 + 3 + ......+ 200 ) =

= 804 + 5 × ( 200 × 201 / 2) =

= 804 + 5 × 100 × 201 =

= 804 + 100 500 =

= 101 304