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Question
Find the sum of all odd positive integers less than 450
Solution
Sum of all odd positive integers less than 450 is given by
1 + 3 + 5 + … + 449
a = 1
d = 2
l = 449
∴ n = `("l" - "a")/"d" + 1`
= `(449 - 1)/2 + 1`
= `448/2 + 1`
= 224 + 1 = 225
∴ Sn = `"n"/2("a" + "l")`
S225 = `225/2(1 + 449)`
= `225/2 xx 450`
= 2252
= 50625
Another method:
Sum of all positive odd integers = n2.
We can use the formula n2 = 2252
= 50625
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