Sum of Natural Numbers
The sum of the first 10, 100, 1000, 10000, and 100000 natural numbers is discussed below.
| Numbers | Sum |
|---|---|
| 1-10 | 55 |
| 1-100 | 5050 |
| 1-1000 | 500500 |
| 1-10000 | 50005000 |
| 1-100000 | 500005000 |
Sum of Square Series
A square series is represented as,
12 + 22 + 32 + 42 + ………. + n2
The sum of n terms of the square series is given using the formula,
Sn = n(n+1)(2n+1)/6
Sum of Cubic Series
A square series is represented as,
13 + 23 + 33 + 43 + ………. + n3
The sum of n terms of the square series is given using the formula,
Sn = [n(n+1)/2]2
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Sum of N Terms of an AP
Arithmetic Sequence is defined as the sequence of numbers such that the difference between any two consecutive numbers is always constant. That is we can say that the next number in the arithmetic sequence is always the previous sequence plus the constant term, where the constant term can be both positive or negative. We can easily find the sum of the first “n” terms of the arithmetic sequence using the formula discussed in the article.
Johann Carl Friedrich Gauss in the 19th century was the first to find the sum of the first “n” terms of the arithmetic sequence where n is any natural number. Let us learn all about the sum of n terms of an AP along with examples in this article.
Table of Content
- What is Sum of n Terms of an AP?
- Sum of n Terms of AP Formula
- Sum of n Terms of AP Proof
- Sum of AP Formula for an Infinite AP
- Sum of AP Formulas
- Sum of Natural Numbers
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