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If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?
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If the sum of the first 30 positive odd integers is k what is the sum ...
Understanding the Sum of Odd Integers
The sum of the first n positive odd integers can be calculated using the formula:
- Sum = n²
For the first 30 positive odd integers:
- n = 30
- Sum = 30² = 900
Thus, k = 900.
Finding the Sum of Non-Negative Even Integers
The first non-negative even integers are 0, 2, 4, 6, ..., up to 2n, where n is the number of terms.
To find the sum of the first n even integers, we can use the formula:
- Sum = n(n + 1)
Here, let's calculate the sum for the first 30 non-negative even integers, which are:
- 0, 2, 4, 6, ..., 58 (total of 30 terms).
Calculation Steps
- For n = 30:
- Sum = 30(30 + 1) = 30 × 31 = 930
Conclusion
The sum of the first 30 non-negative even integers is 930.
Final Thoughts
- Sum of the first 30 positive odd integers = 900
- Sum of the first 30 non-negative even integers = 930
This demonstrates a fundamental relationship between odd and even integers in arithmetic sequences.
The sum of the first n positive odd integers can be calculated using the formula:
- Sum = n²
For the first 30 positive odd integers:
- n = 30
- Sum = 30² = 900
Thus, k = 900.
Finding the Sum of Non-Negative Even Integers
The first non-negative even integers are 0, 2, 4, 6, ..., up to 2n, where n is the number of terms.
To find the sum of the first n even integers, we can use the formula:
- Sum = n(n + 1)
Here, let's calculate the sum for the first 30 non-negative even integers, which are:
- 0, 2, 4, 6, ..., 58 (total of 30 terms).
Calculation Steps
- For n = 30:
- Sum = 30(30 + 1) = 30 × 31 = 930
Conclusion
The sum of the first 30 non-negative even integers is 930.
Final Thoughts
- Sum of the first 30 positive odd integers = 900
- Sum of the first 30 non-negative even integers = 930
This demonstrates a fundamental relationship between odd and even integers in arithmetic sequences.
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If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?
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If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?.
If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?.
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