Difference Series

One the differences of whose succe ive terms either are constant, or form a series whose differences as before are constant, or form a third series, ultimately resting upon a constant difference. The order of the series depends upon the number of steps prior to the constant relation. A series of the first order has its first difference constant and is an arithmetical progre ion. Analysis of the series gives: where a is the first term, d, d, d, etc. to dn the first terms of the succe ive differences and n the number of terms (the last term) an=a+(n-1) d,+ (n-1)(n-2) d. L2 (n-1) (n-2) (n-3) d3 + etc., and for the sum of in terms L3 n(n-1) d1n(n-1)(n-2) d, Sn-na+ +etc. To solve a L2 L3 difference series of the nth order (n + 1) consecutive terms must be given. Differential. The differential of a function or variable at any value is what would be its increment in any interval of for a differential is the letter d placed immediately before the function or variable, as du, d(x2), read differential of u, differential of x2. IMG:content-1157.png:[blocks in formation]