Question

va rog calculati-mi si mie 2+4+6+...+42, 1+3+5+....+73, 5+10+15+..+145

Answer 1

2 + 4 + 6 + ...... + 42 = 462

= 2 × 1 + 2 × 2 + 2 × 3 + ..... + 2 × 21 =

= 2 × ( 1 + 2 + 3 + ....... + 21 ) =

= 2 × 21 × ( 1 + 21 ) : 2 =

= 21 × 22 =

= 462

__________________________

1 + 3 + 5 + 7 + ...... + 73 =

= 37 × ( 1 + 73 ) : 2 =

= 37 × 74 : 2

= 37 × 37 =

= 1 369

sau:

= 1 + ( 1 + 2 ) + ( 1 + 4 ) + ( 1 + 6 ) + ......... + ( 1 + 72 ) =

( 73 - 1 ) : 2 + 1 = 72 : 2 + 1 = 36 + 1 = 37 termeni are suma

= 1 × 37 + 2 × ( 1 + 2 + 3 + ........ + 36 ) =

= 37 + 2 × 36 × ( 1 + 36 ) : 2 =

= 37 + 36 × 37 =

= 37 × ( 1 + 36 ) =

= 37 × 37 =

= 1 369

_______________________

5 + 10 + 15 + .......+ 145 = 2 175

= 5 × 1 + 5 × 2 + 5 × 3 + ....... + 5 × 29 =

= 5 × ( 1 + 2 + 3 + ....... + 29 ) =

= 5 × 29 × ( 1 + 29 ) : 2 =

= 145 × 30 : 2 =

= 145 × 15 =

= 2 175