Răspuns:
Explicație pas cu pas:
a)
2 + 4 + 6 + ..... + 1000 = 250 500
= 2 × ( 1 + 2 + 3 + .... + 500 ) =
= 2 × 500 × ( 1 + 500 ) : 2 =
= 500 × 501 =
= 250 500
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b)
4 + 8 + 12 + ..... + 1 000 =125 500
= 4 × ( 1 + 2 + 3 + ...... + 250 ) =
= 4 × 250 × ( 1 + 250 ) : 2 =
= 2 × 250 × 251 =
= 500 × 251 =
= 125 500
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c)
1 + 3 + 5 + .......+ 99 = 2 500
( 99 - 1 ) : 2 + 1 = 98 : 2 + 1 = 50 termeni are suma numerelor impare cu primul termen 1
= 50 × ( 1 + 99 ) : 2 =
= 50 × 100 : 2 =
= 50 × 50 =
= 2 500
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d)
1 + 3 + 5 + ....... + 2019 =
( 2019 - 1 ) : 2 + 1 = 2018 : 2 + 1 = 1009 + 1 = 1 010 termeni are suma
= 1010 × ( 1 + 2019 ) : 2 =
= 1010 × 2020 : 2 =
= 1010 × 1010 =
= 1010²=
= 1 020 100
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e)
17 + 34 + 51 + ...... + 11713 =
= 17 × ( 1 + 2 + 3 + ..... + 689 ) =
= 17 × 689 × ( 1 + 689 ) : 2 =
= 11 713 × 690 : 2 =
= 11 713 × 345 =
= 4 040 985
