To find the sum of odd integers in the range from 0 to 298, we need to determine the number of odd integers in that range and then calculate their sum.
The first odd integer in the range is 1, and the last odd integer is 297. The odd integers in this range can be represented as 1, 3, 5, 7, …, 297.
To find the number of odd integers in this sequence, we can use the formula for the nth term of an arithmetic sequence: an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference.
In this case, a1 = 1, d = 2 (since we are adding 2 to each term to get the next odd integer), and an = 297. We can rearrange the formula to solve for n:
297 = 1 + (n-1)2 296 = 2n - 2 298 = 2n n = 298/2 n = 149
So, there are 149 odd integers in the range from 0 to 298.
To find the sum of these odd integers, we can use the formula for the sum of an arithmetic series: Sn = (n/2)(a1 + an), where Sn is the sum, n is the number of terms, a1 is the first term, and an is the last term.
Plugging in the values, we get:
Sn = (149/2)(1 + 297) Sn = (149/2)(298) Sn = 149 * 149 Sn = 22,201
Therefore, the sum of the odd integers in the range from 0 to 298 is 22,201.
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