Easiest math problem ever

Algebra Level 2

If 1 + 2 + 3 + ⋯ + 100 = x 1 + 2 + 3 + \cdots + 100 = x , find the value of 2 x 101 \dfrac{2x}{101} .

50 5050 non-rational number 100

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Ash R by Ash R , 16, USA

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2 solutions

1 + 2 + … + 100 = 100 × 101 2 = x 1+2+\ldots +100=\dfrac{100\times101}{2}=x . Hence 2 x 101 = 2 × 101 × 100 2 × 101 = 100 \dfrac{2x}{101}=\dfrac{2 \times 101 \times 100}{2 \times 101}=\boxed{100} .

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1 + 2 + 3 + . . . + 100 = x 1 + 2 + 3 + . . . + 100 = x

S = x = n 2 ( a 1 + a n ) = 100 2 ( 1 + 100 ) = 5050 S=x=\dfrac{n}{2}(a_1 + a_n)=\dfrac{100}{2}(1 + 100) = 5050

It follows that,

2 x 101 = 2 × 5050 101 = 100 \dfrac{2x}{101} = \dfrac{2 \times 5050}{101} = \color{#69047E}\boxed{100}

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