Series Formulas - mathportal.org

Series Formulas 1. Arithmetic and Geometric Series Definitions: First term: a1 Nth term: an Number of terms in the Series : n Sum of the first n terms: Sn Difference between successive terms: d Common ratio: q Sum to infinity: S Arithmetic Series Formulas : ()11naand=+ 112iiiaaa ++= 12nnaaSn+= ()1212nandSn+ = Geometric Series Formulas : 11nnaa q = 11iiiaaa += 11nna q aSq = ()111nna qSq = 1111foaSqrq <<= 2. Special Power Series Powers of Natural Numbers ()1112nkkn n==+ () ()2111 2 16nkkn nn==++ ()2321114nkkn n==+ Special Power Series ()2311..11:1x xxxxfor= + +++ < < ()2311..11:1x xxxxfor= + + < <+ 231..2! 3!xxxex= + +++ ()()2345ln 1..112 3 4 5:xxxxxorxxf+= + + < < 3579sin..3! 5! 7! 9!xxxxx x= + + 2468cos 1..2! 4! 6! 8!xxxxx= + + 3572 .3 15 31522:forxxxx xx = ++++ < < 3579sinh..3! 5! 7! 9!xxxxx x= ++++ 2468cosh 1.

Series Formulas 1. Arithmetic and Geometric Series Definitions: First term: a 1 Nth term: a n Number of terms in the series: n Sum of the first n terms: S n Difference between successive terms: d Common ratio: q Sum to infinity: S Arithmetic Series Formulas: a a n dn = + −1 (1) 1 1 2 i i i a a a − + + = 1 2 n n a a S n + = ⋅ 2 11 ( ) n 2 ...

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