Question

Sum of series : 1+2+3+ …………………… + n is

()
(+1)
/2

() ( + 1)
()
(+1)(+2)/
2

() none of these.
Ft​

Answer 1

Answer:

n(n+1)/2

Step-by-step explanation:

sum of series:1+2+3+............+n is n(n+1)/2

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Answer 2

Given:

• A sum of series upto n terms 1+2+3+4+5+.........+n .

To Find:

• A equivalent formula for the sum of series.

Answer:

Given sum of series is 1+2+3+4+5+....+n.

So the series will be 1,2,3,4,5,.......n

Here

• First term is 1 . (a)
• Total number of terms is n. (n)
• Common Difference is 1. (d)

So , using formula of AP ,

$\red{\sf{\leadsto S_{n}=\dfrac{n}{2}[2a+(n-1)d]}}$

$\sf{\implies S_{n}= \dfrac{n}{2}[2\times1+(n-1)1]}$

$\sf{\implies S_{n}= \dfrac{n}{2}[2+(n-1)]}$

$\sf{\implies S_{n}=\dfrac{n}{2}[2-1+n]}$

${\underline{\boxed{\red{\sf{\longmapsto S_{n}=\dfrac{n(n+1)}{2}}}}}}$

Hence the sum of series is n(n+1)/2.