UPSC Exam > UPSC Questions > The sum of the first n terms of the series 1 ...
Start Learning for Free
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is?
Most Upvoted Answer
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2...
Explanation:
Given Series:
1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +...
Sum of the First n Terms:
The sum of the first n terms of the series is given by the formula: (n * (n + 1) ^ 2) / 2
When n is Odd:
When n is odd, the sum of the first n terms can be calculated using the formula above. Let's consider n = 3 as an example:
Sum = (3 * (3 + 1) ^ 2) / 2
Sum = (3 * 4 ^ 2) / 2
Sum = (3 * 16) / 2
Sum = 48 / 2
Sum = 24
Therefore, when n is odd, the sum of the first n terms will be an even number, as shown in the example above.
Explanation:
- The sum of the first n terms of the series is given by the formula: (n * (n + 1) ^ 2) / 2
- When n is odd, the sum will always be an even number.
- This is because the product of an odd number and any number (odd or even) is always even.
- Thus, the sum of the first n terms of the series will be an even number when n is odd.
Given Series:
1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +...
Sum of the First n Terms:
The sum of the first n terms of the series is given by the formula: (n * (n + 1) ^ 2) / 2
When n is Odd:
When n is odd, the sum of the first n terms can be calculated using the formula above. Let's consider n = 3 as an example:
Sum = (3 * (3 + 1) ^ 2) / 2
Sum = (3 * 4 ^ 2) / 2
Sum = (3 * 16) / 2
Sum = 48 / 2
Sum = 24
Therefore, when n is odd, the sum of the first n terms will be an even number, as shown in the example above.
Explanation:
- The sum of the first n terms of the series is given by the formula: (n * (n + 1) ^ 2) / 2
- When n is odd, the sum will always be an even number.
- This is because the product of an odd number and any number (odd or even) is always even.
- Thus, the sum of the first n terms of the series will be an even number when n is odd.
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
|
|
Top Courses for UPSCView all
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is?
Question Description
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is?.
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is?.
Solutions for The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? 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 The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? defined & explained in the simplest way possible. Besides giving the explanation of
The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is?, a detailed solution for The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? has been provided alongside types of The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? theory, EduRev gives you an
ample number of questions to practice The sum of the first n terms of the series 1 ^ 2 + 2.2 ^ 2 + 3 ^ 2 + 2.4 ^ 2 + 5 ^ 2 + 2.6 ^ 2 +... is (n * (n + 1) ^ 2)/2 even. When n is odd the sum is? 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