Question

S=1 + 3 + 5 +...+123
S=?

S=1+3+5+...+555
S=?

Answer 1

s=1+3+5+...+123 mai intai aflam nr.de termeni astfel

n=(123-1):2 +1=61+1=62

aplicam formula gaus

s=(123+1)*62/2=124*31=3844

s=1+3+5+......+555

n=(555-1):2+1=278

s=(555+1)*278/2=77284

Answer 2

S = 1 + 3 + 5 + ..... + 123

→ stabilesc cati termeni are suma cu ratia 2

( 123 - 1 ) : 2 + 1 = 122 : 2 + 1 = 61 + 1 = 62 termeni

→ aplic formula sumei lui Gauss

= 62 × ( 1 + 123 ) / 2 =

= 31 × 124 =

S = 3 844

____________________________

S = 1 + 3 + 5 + ...... + 555

→ stabilesc cati termeni are suma cu ratia 2 ( 3 - 1 = 2;   5 - 3 = 2; .... )

( 555 - 1 ) : 2 + 1 = 554 : 2 + 1 = 277 + 1 = 278 termeni

S = 278 × ( 1 + 555 ) / 2

S = 139 × 556

S = 77 284