Question

Aflați pe x din egalitatea x+1+3+3+7+9+...+100=2+4+6+8+10+...+200​

Answer 1

Răspuns: x = 7 500

Explicație pas cu pas:

x+1+3+5+7+......+99+100 = 2+4+6+......+200

x+1+3+5+7+.....+99+100 = 2×(1+2+3+4+5+......+100)

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Aflam suma numerelor impare:

1+3+5+7+.....+99 = 50×100:2 = 50²= 2500

(99-1):2+1=98:2+1=50 termeni are suma

x + 2500 + 100 = 2×(100×101) : 2

x + 2 600 = 100 × 101

x = 100 × 101 - 2600

x = 10 100 - 2 600

x = 7 500

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Sau:

x = 2+4+6+8+..............+100+102+......+200

    -1 -3 -5 -7 -             - 99 - 100

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x = 1 +1 +1 +1 +................. + 1 + 2 + 104 + .....+200

(99-1):2+1 = 50 termeni

-> 50 diferenta de 1

104 + 106 + 108 + .....+200 = 49 ×(104+200):2 = 49 ×304:2

(200-104): 2+1 =96:2+1=49 termeni mai are suma

x = 50×1 + 2+  49×152

x = 52 + 7448

x = 7500