An algebra problem by Shintaro Inaba

Algebra Level 1

1 + 2 + 3 + 4 + 5 + 6 + ⋯ + 99 + 100 = ? 1+2+3+4+5+6+\cdots+99+100= \, ?


The answer is 5050.

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Shintaro Inaba by Shintaro Inaba , 17, Japan

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2 solutions

Simply,

Let S = 1 + 2 + 3 + 4.. + 99 + 100 S = 1+2+3+4..+99+100 and

S = 100 + 99 + 98 + 97.. + 2 + 1 S = 100 +99+98+97..+2+1

Adding both the equations,

2 S = 101 + 101 + 101 … 2S = 101+101+101… 100 times,

2 S = 101 × 100 2S= 101×100

S = 5050 S=5050

2 Helpful 1 Interesting 0 Brilliant 0 Confused

Ramarjunam used exact same method when this concept came to life 👍🏻

Suraj Jha - 7 months ago
Ashish Menon
Jun 2, 2016

The answer is 100 × 101 2 = 5050 \dfrac{100 × 101}{2} = \color{#69047E}{\boxed{5050}} .

2 Helpful 0 Interesting 0 Brilliant 0 Confused

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