Question

8. Calculează: a) (1+2+...+50)+(1+2+3+...+200); c) 2+4+64 b) 31 +32 +33 +...+100; d) 1+3+5+...+99. +100;
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Answer 1

Răspuns:

a) ( 1 + 2 +........+50 ) + ( 1 + 2 + 3 +........+ 200 )

1 + 2 +........+50 = ( 1 + 50 ) × 50 : 2

= 51 × 25

= 1275

1 + 2 + 3+ .........+ 200 = ( 1 + 200 ) × 200 : 2

= 201 × 100

= 20100

1275 + 20100 = 21375

b) 31 + 32 + 33 + .......... + 100 =

Aflăm nr de termeni

( 100 - 31 ) + 1 = 69 + 1 = 70 termeni

S = ( 31 + 100 ) × 70 : 2

S = 131 × 35

S = 4585