Question

b)(2+4+...+200)÷((4+8+...100)÷13); c) (1+2+...+300)÷903;d)(8+16+...344)÷(4+8+...+172;

Answer 1

Rezolvarea e în poză

Answer 2

b)  

( 2 + 4 + ........ + 200 ) : [ ( 4 + 8 + ........ + 100 ) : 13 ] = 101

= 2 × ( 1 + 2 + ...... + 100 ) : [ 4 × ( 1 + 2 + ..... + 25 ) : 13 ] =

= [2 × 100 × ( 1 + 100 ) : 2 ] : [ 4 × 25 × ( 1 + 25 ) : 2 : 13 ] =

= ( 100 × 101 ) : ( 2 × 25 × 2 ) =

= 10 100 : 100 =

= 101

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c)

( 1 + 2 + ....... + 300 ) : 903 = 50

= 300 × ( 1 + 300 ) : 2 : 903 =

= 150 × 301 : 903 =

=  150 : 3 =

=  50

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d)

( 8 + 16 + ...... + 344 ) : ( 4 + 8 + ..... + 172 ) = 2

= 8 × ( 1 + 2 + .......... 43 ) : [ 4 × ( 1 + 2 + .... + 43 ) ] =

= (  8 × 43 × ( 1 + 43 ) : 2 ] : [ 4 × 43 × ( 1 + 43 ) : 2 ] =

= ( 4 × 43 × 44 ) : ( 2 × 43 × 44 ) =

= 2