##### How to derieve the formula for sum of series

I'm able to analyze and solve the equation till i get some specific series like **T(n)=1+2+3+...n** and other type of series but i'm unable to know how to determine the formula for the series derieved like **sum of 1st n natural numbers is said to be n(n-1)/2** so how to derieve formula's for any series

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