Question

Suma gauss la 95+96+97+...+304

Answer 1

Răspuns:

Explicație pas cu pas:

Primul mod:

( 1 + 2 + 3 + ...... + 94 + 95 + .....+ 304 ) - ( 1 + 2 + 3 + ..... + 94 ) =

= 304 × (1+304) : 2 - [ 94 × ( 1 + 94 ) : 2 ] =

= 152 × 305 - ( 47 × 95 ) =

= 46 360 - 4 465 =

= 41 895

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Al doilea mod:

95 + 96 + 97 + ..... + 304 = 41 895

304 - 95 + 1 = 210 termeni are suma

= 210 × ( 95 + 304 ) : 2 =

= 105 × 399 =

= 41 895

Answer 2

95 + 96 + 97 + ... + 304 =

[ ( 304 - 95 + 1 ) × ( 95 + 304 ) ] : 2 =

[ ( 209 + 1 ) × 399 ] : 2 =

( 210 × 399 ) : 2 =

83790 : 2 = 41895