Question

2+3+4+....+50=
1+2+3+....+500=
1+97+2+999+3+198=
1+2+3+.....+124=
2+4+6+....+600=
15+16+17+...+70=
PLS!!!

Answer 1

2 + 3 + 4 + .... + 50 = 49 × ( 2 + 50 ) / 2 = 49 × 52 / 2 = 49 × 26 = 1 274  

1 + 2 + 3 + .... + 500 =  500 × ( 1 + 500 ) / 2 = 250 × 501 = 125 250  

1 + 97 + 2 + 999 + 3 + 198 = 1 300

=   ( 1 + 999 ) + ( 2 + 198 ) + ( 97 + 3 ) =

= 1 000 + 200  + 100 =

= 1 300

_________________

1 + 2 + 3 + ..... + 124 =  124 × ( 1 + 124 ) : 2 = 62 × 125 = 7 750

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2 + 4 + 6 + .... + 600 =  2 × ( 1 + 2 + 3 + ...... + 300 ) = 90 300

= 2 × 300 × 301 / 2 =

= 300 × 301 =

= 90 300

_____________________________

15 + 16 + 17 + ... + 70 = 1 988

70 - 15 + 1 = 56 termeni are suma

= 56 × ( 1 + 70 ) / 2 =

= 28 × 71 =

= 1 988