Question

Ajutați-mă vă rog cu următoarele exerciții cu metoda gaaus + factorul comun.

Answer 1

S = 54 + 63 + 72 + 81 + ........ + 675

S = 9 × ( 6 + 7 + 8 + 9 + ...... + 75 )

→ stabilesc cati termeni are suma cu ratia = 1 ( 6 - 7 = 1;  8 - 7 = 1; .... )

75 - 6 + 1 = 69 + 1 = 70 termeni are suma

→ aplic formula sumei lui Gauss

S = 9 × 70 × ( 6 + 75 ) : 2

S = 9 × 35 × 81

S = 25 515

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S = 10 + 15 + 20 + 25 + ...... + 315

S = 5 × ( 2 + 3 + 4 + 5 +...... + 63 )

S = 5 × ( 63 - 2 + 1 ) × ( 2 + 63 ) : 2

S = 5 × 62 × 65 : 2

S = 325 × 31

S = 10 075

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S = 52 + 60 + 68 + 76 + ...... + 540

S = 2 × ( 26 + 30 + 34 + 38 + ...... + 270 )

→ stabilesc cati termeni are suma cu ratia = 4 ( 30 - 26 = 4;   34 - 30 = 4;..... )

( 270 - 26 ) : 4 + 1 = 244 : 4 + 1 = 62 termeni are suma

→ aplic formula sumei lui Gauss

S =2 × 62 × ( 26 + 270 ) : 2

S = 62 × 296

S = 18 352

__________________________

S = 19 + 38 + 57 + 76 + ...... + 665

S = 19 × ( 1 + 2 + 3 + 4 + ...... + 35 )

S = 19 × 35 × 36 : 2

S = 665 × 18

S = 11 970  

Answer 2

Rezolvarea in atasamnet