Question

write a short form of the expansion in symbolic form 1+2+3+4+.......+n​

Answer 1

Step-by-step explanation:

1+2+3+4+is x+n is 10is the expansion symbolic

Answer 2

The short form would be $\dfrac{n(n+1)}{2}$

Step-by-step explanation:

Given series,

1+2+3+4+.......+n​

Since, the difference between two consecutive terms is constant ( i.e. 1 )

Average of the number = $\frac{\text{First number +Last number}}{2}$

$=\frac{1+n}{2}$

$=\frac{n+1}{2}$

Total numbers = n,

Thus, the total sum =  total numbers × average

$=\dfrac{n(n+1)}{2}$

Which is the required short form.

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