Question

Dau 50 de puncte !

calculati urmatoarele sume :
a) 2 +4+6+.....+1000

b) 4+8+12+.....+1000

c) 1+3+5+...+99

d)1+3+5+....+2019

e) 17+34+51+....+11713
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Answer 1

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