Question

S6=3+6+....+63+66

S7=5+10+15+....+95+100

S4=1+3+5+....+97+99

Answer 1

S₆ = 3 + 6 + ...... + 63 + 66

S₆ = 3 x ( 1 + 2 + ...... + 21 + 22 )

S₆ = 3 x 22 x 23 : 2

S₆ = 3 x 11 x 23

S₆ = 759

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S₇ = 5 + 10 + 15 + .... + 95 + 100

S₇ = 5 x ( 1 + 2 + 3 + ..... + 19 + 20 )

S₇ = 5 x 20 x 21 : 2

S₇ = 5 x 10 x 21

S₇ = 1 050

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S₄ = 1 + 3 + 5 + ....... + 97 + 99

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

( 99 - 1 ) : 2 + 1 = 50 termeni are suma

→ aplic formula sumei lui Gauss

S₄= 50 × ( 1 + 99 ) : 2

S₄ = 50 × 50

S₄ = 2 500

Answer 2

S6=3(1+2+...21+n)=3n(n+1)/2
S6=(3*22*23)/2
S6=3*11*23
S6=33*23
S6=759

S7=5(1+2+3+......+19+n)=5n(n+1)/2
S7=(5*20*21)/2
S7=50*21
S7=1050

La s4 nu stiu