at http://tutorial.math.lamar.edu/Classes/CalcII/ConvergenceOfSeries.aspx in example number 1 how Sn= Summation from i=1 to n of i suddenly becomes n(n+1)/2 how did it happen?

Question

anonymous · Answer

That is an established formula for the sum of the first n numbers.  Think of it this way:  The first and the last numbers sum to n+1, as do the second and n-1 number, etc.  There are n/2 of these pairs, so the overall sum is n(n+1)/2.

anonymous · Answer

ok got it ........ if 1+ 2 = 3 then according to this formula the answer will be same i.e. 3

anonymous · Answer

isn't?

anonymous · Answer

Yeah, it is.  2*3/2=3

anonymous · Answer

thanks mate

anonymous · Answer

Usually use the formula for longer strings of numbers to be summed, but it works right down to the beginning of the list.

anonymous · Answer

No sweat; glad to help.

anonymous · Answer

btw why the heck series is covered in calculus? does it have any use in real analysis~?

anonymous · Answer

Used ALL THE TIME in Real, Complex, Applied, and Numerical analysis, as well as Diff EQ.

anonymous · Answer

okkkkkk so i will have to study it :(