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Sequences, partial sums The n-th partial sum sn of a sequence of numbers (an) is the sum of the sequence members from a1 to an. The ever continuing partial sum of an (infinite) number sequence - Domyhomework will do your assignments - is called an (infinite) series. A function whose domain is the set of natural numbers (or a subset thereof) and which has a subset of the real numbers as its domain is called a (real) number sequence - homework help in algebra . Mathematically significant are the so-called partial sums of number sequences. The n-th partial sum sn of a sequence of numbers (an) is the sum of the members from a1 to an or (written differently) sn=∑i = 1na i. For some sequences it is relatively easy to give formulas for the calculation - do my economics assignment - of the partial sums (see also calculation example 1). We consider two examples in the following. Example 1:an=an-1+2; a1=2 resp. an=2n (n=1, 2; 3 ...) We can see that the partial sums become larger and larger with increasing n and finally grow beyond all limits: s1=a1=2s2=a1+a2=s1+a2=2+4=6s3=a1+a2+a3=s2+a3=6+6=12...sn=a1+a2+...+an=n2(2+2n)=n2+n Example 2: an=an - 12; a1=1 or an=12n - 1=21 - n (n=1, 2; 3 ...). In this example, the partial sums also become larger with increasing n, but (as the following formula shows) they always remain below the value 2: s1=1; s2=1+12=32=1.5; s3=32+14=74=1.75;s4=74+18=158=1.875 ...sn=2-12n - 1 The ever continuing partial sum of an (infinite) number sequence is called an (infinite) series. Useful Resources: The main cause of particulate matter: essay Basic idea of liberalism Creating a website concept / brainstorming ideas Arithmetic sequences Geometric sequences

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