Series

• $\sum ^n _ {r=1}$k f(r) = k $\sum ^n _ {r=1}$f(r), and $\sum ^n _ {r=1}$f(r) + g(r) = $\sum ^n _ {r=1}$f(r) + $\sum ^n _ {r=1}$g(r).
• $\sum ^n _ {r=k}$f(r) = $\sum ^n _ {r=1}$f(r) - $\sum ^ {k-1} _ {r=1}$f(r).
• $\sum ^n _ {r=1}$1 = n, and $\sum ^n _ {r=1}$r = 1/2 n (n + 1). (given in FB).
• $\sum ^n _ {r=1}$$r^2$ = 1/6 n (n + 1)(2n +1) and $\sum ^n _ {r=1}$$r^3$ = 1/4 $n^2$ $(n + 1)^2$.
• Method of differences involves rewriting the general term of a series as a difference of two or more terms in order to calculate the sum easier as many terms will cancel out periodically.
• The Maclaurin series of a given function is an infinite sum of terms that estimates what a function looks like around x = 0. The formulas are in the formula book, and it is only valid when the values of x cause the series to converge and the derivatives of the function are real.