Question

a
24+25+26.....+198+199
b

1+6+11......+96+101

Answer 1

a) 24 + 25 + 26 + .... + 198 + 199 = 19 624

→ stabilesc cati termeni are suma cu ratia = 1 ( 25 - 24 = 1;   26 - 25 = 1; ....)

199 - 24 + 1 = 176 termeni are suma

→ aplic formula sumei lui Gauss

= 176 × ( 24 + 199 ) / 2 =

= 88 × 223 =

= 19 624

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b)  1 + 6 + 11 + ...... + 96 + 101 = 1 176

→ ratia = 5;

( 101 - 1 ) : 5 + 1 = 100 : 5 + 1 = 21 termeni are suma

= 21 × ( 1 + 101 ) / 2 =

= 21 × 112 / 2 =

= 21 × 56 =

= 1 176