Răspuns:
Explicație pas cu pas:
a) 1 + 3 + 5 + ...... + 2019 =
→ stabilesc cati termeni are suma numerelor impare:
( 2019 - 1 ) : 2 + 1 = 1009 + 1 = 1010 termeni
= 1010 × ( 1 + 2019) : 2 = → aplic formula sumei lui Gauss
= 1010 × 1010 =
= 1010² =
= 1 020 100
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b)
2 + 4 + 6 + .... + 2018 + 2019 =
2 × ( 1 + 2 + 3 + ..... + 1009 ) + 2019 =
= 2 × 1009 × (1+1009) : 2 + 2019 =
= 1009 × 1010 + 2019 =
= 1 019 090 + 2019 =
= 1 021 109
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c)
4 + 8 + 12 + .....+ 2020 =
= 4 × ( 1 + 2 + 3 + ....... + 505 ) = → l-am dat factor comun pe 4
= 4 × 505 × ( 1+505) : 2 = → am aplicat formula sumei lui Gauss
= 2 × 505 × 506 =
= 1010 × 506 =
= 511 060
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d)
5 + 10 + 15 + ..... + 2025 =
= 5 × ( 1 + 2 + 3 + ..... + 405 ) =
= 5 × 405 × ( 1 + 405 ) : 2 =
= 2 025 × 203 =
= 411 075
