Question:
Let $ V_r $ denote the sum of the first $ r $ terms of an arithmetic progression $ (AP) $ whose first term is $ r $ and the common difference is $ (2r - 1) $ . The sum $ V_1 + V_2 + ..... + V_n $ is
Let $ V_r $ denote the sum of the first $ r $ terms of an arithmetic progression $ (AP) $ whose first term is $ r $ and the common difference is $ (2r - 1) $ . The sum $ V_1 + V_2 + ..... + V_n $ is
Updated On: Jun 14, 2022
- $ \frac{1}{12} n (n + 1 ) (3n^2 - n + 1) $
- $ \frac{1}{12} n (n + 1 ) (3n^2 + n + 2) $
- $ \frac{1}{2} n (2n^2-n-1) $
- $ \frac{1}{3} (2n^3 - 2n + 3) $
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The Correct Option is B
Solution and Explanation
Answer (b) $ \frac{1}{12} n (n + 1 ) (3n^2 + n + 2) $
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Concepts Used:
Series
A collection of numbers that is presented as the sum of the numbers in a stated order is called a series. As an outcome, every two numbers in a series are separated by the addition (+) sign. The order of the elements in the series really doesn't matters. If a series demonstrates a finite sequence, it is said to be finite, and if it demonstrates an endless sequence, it is said to be infinite.
Read More: Sequence and Series
Types of Series:
The following are the two main types of series are: