An algebra problem by Joey Guan

Algebra Level 1

1 + 2 + 3 + ⋯ + 50 = ? \large 1 + 2 + 3 + \cdots + 50 = \, ?

1607 1499 1358 1500 1275

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Joey Guan by Joey Guan , 21, Canada

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2 solutions

Viki Zeta
Sep 21, 2016

S = 1 + 2 + 3 + … + 50 S = 50 + 49 + 48 + … + 1 2 S = 51 + 51 + 51 + … + 51 2 S = 50 × 51 S = 50 × 51 2 = 1275 S = 1 + 2 + 3 + \ldots + 50 \\ S = 50 + 49 + 48 + \ldots + 1 \\ 2S = 51 + 51 + 51 + \ldots + 51 \\ 2S = 50 \times 51 \\ S = \dfrac{50 \times 51}{2} = 1275

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Dhruv Singh
Sep 21, 2016

1 + 2 + 3...+ 50

we can now make pairs such as,

(1+49) + (2+48) + ... + (24+26) + 25 + 50

so we get,

50 + 50 + ..... + 50 + 25

hence we get 25 pairs of 50 plus 25 (you cannot form a pair of 25)

25*50 + 25

1250 + 25

ANS = 1275

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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