Question

HELPPPP,CN MA AJUTA PRIMESTE COROANA​

Answer 1

Folosim suma lui Gauss:

$1+2+3+...+n=n(n+1):2$

a)

calculam intai paranteza

1+2+3+...+98=98×99:2=4851

x=98×99+99

x=99(98+1)

x=9801

b)

1+2+3+...+49=49×50:2=1225

x=8×1225+1225

x=1225×9=11025

c)

Dam factor comun pe 2

x=2(1+2+3+...+324)-324²

x=324×325-324²

x=324(325-324)=324

d)

x=1+2+3+...+224+16×450

x=224×225:2+16×450

x=112×225+16×450

x=225(112+32)

x=32400

e)

Factor comun 2

x=2(1+2+3+...+225)-225²

x=225×226-225²

x=225(226-225)

x=225

f)

x=3(1+3+5+...+99)-5000

Calculam suma numerelor totale de la 1 la 99

99×100:2=99×50

Calculam suma numerelor pare de la 1 la 99

2(1+2+...+49)=49×50

1+3+5...+99=99×50-49×50=50(99-49)=50²

x=3×50²-5000

x=2500

g)

Dam factor comun pe 2

x=2(1+2+3+...+50)-25×2

x=50×51-50

x=50(51-1)

x=50²=2500

h)

x=120×121:2+2×242

x=60×121+2×242

x=121(60+4)

x=7744

Un alt exercitiu gasesti aici: https://brainly.ro/tema/1183972

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