Question

30+60+90+120+...+900,21+42+63+84+...2100

Answer 1

30 + 60 + 90 + 120 + ...... + 900 = 13 950

=30 × ( 1 + 2 + 3 + 4 + ...... + 30 ) =

= 30 × 30 × ( 1 + 30 ) : 2 =

= 15 × 30 × 31 =

= 15 × 930 =

= 13 950

____________________________

21 + 42 + 63 + 84 + ..... + 2 100 = 106 050

= 21 × ( 1 + 2 + 3 + 4 + ...... + 100 ) =

= 21 × 100 × ( 1 + 100) : 2 =

= 21 × 50 × 101 =

= 1 050 × 101 =

= 106 050

Answer 2

30+60+90+120+...+900=
=30×(1+2+3+......+900:30)=
=30×(1+2+3+......+30)=
=30×[30×(30+1):2]=
=30×(30×31:2)=
=30×(930:2)=
=30×465=
=13950





21+42+63+84+...+2100=
=21×(1+2+3+........+2100:21)=
=21×(1+2+3+.....+100)=
=21×[100×(100+1):2]=
=21×(100×101:2)=
=21×(10100:2)=
=21×5050=
=106050