What is the Sum of 1 2 3 N-

Find the sum of 1, 2 ,3, ⋯ ,nThe given number series is 1, 2 ,3, ⋯ ,n.It is a series of natural numbers. The sum of first nterms of an Ap series is n/2[2a+(n ...

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Standard XII

Mathematics

Sum of n Terms

What is the S...

Question

What is the sum of $1, 2, 3, \dots, n$ ?

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Solution

Find the sum of $1, 2, 3, \dots, n$
The given number series is $1, 2, 3, \dots, n$ .
It is a series of natural numbers.
The sum of first $n$ terms of an Ap series is $\frac{n}{2} [2 a + (n - 1) d]$ , where $a$ is the first term, $d$ is common difference and $n$ is the number of term.
The first term of the series is $1$ .
The common difference is $2 - 1 = 3 - 2 = 1$
The sum of the series is $\frac{n}{2} \{2 \cdot 1 + (n - 1) \cdot 1\}$
$= \frac{n}{2} (2 + n - 1)$
$= \frac{n (n + 1)}{2}$
Hence the sum of $1, 2, 3, \dots, n$ is $\frac{n (n + 1)}{2}$ .

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What is the sum of 1,2,3,⋯,n?

What is the sum of $1, 2, 3, \dots, n$ ?