If x is the sum of the odd numbers from 1 to 100 and y is the sum of the even numbers from 1 to 100, which is greater, x or y? By how many?
回答 (2)
2016-06-21 3:00 pm
Let S₁ be the sum of odd numbers from 1 to 100, and S₂ be the sum of even numbers from 1 to 100.
S₁ = 1 + 3 + 5 + ...... + 99
S₂ = 2 + 4 + 6 + ...... + 100
S₂ - S₁
= (2 - 1) + (4 - 3) + (6 - 5) + ...... (100 - 99)
= 1 × 50
= 50
From 1 to 100, the sum of even numbers is greater than that of odd numbers by 50.
S₁ = 1 + 3 + 5 + ...... + 99
S₂ = 2 + 4 + 6 + ...... + 100
S₂ - S₁
= (2 - 1) + (4 - 3) + (6 - 5) + ...... (100 - 99)
= 1 × 50
= 50
From 1 to 100, the sum of even numbers is greater than that of odd numbers by 50.
2016-06-21 2:56 pm
S = (n/2) * (t[1] + t[n])
Each sequence has 50 terms
(50/2) * (1 + 99) => 25 * 100 = 2500
(50/2) * (2 + 100) => 25 * 102 = 2550
2550 - 2500 = 50
Each sequence has 50 terms
(50/2) * (1 + 99) => 25 * 100 = 2500
(50/2) * (2 + 100) => 25 * 102 = 2550
2550 - 2500 = 50
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