UPSC Exam > UPSC Questions > If the sum of the first 30 positive odd integ...
Start Learning for Free
If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?
Most Upvoted Answer
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.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?
Question Description
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?.
Solutions for If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? defined & explained in the simplest way possible. Besides giving the explanation of
If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers?, a detailed solution for If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? has been provided alongside types of If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? theory, EduRev gives you an
ample number of questions to practice If the sum of the first 30 positive odd integers is k what is the sum of the first non negative even intergers? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup