Consequences, general



Consequences, general

A function whose definition domain – pay someone to do my assignment –  is the set of natural numbers (or a subset thereof) and which has a subset of the real numbers as its value domain is called a (real) number sequence.

The n-th partial sum of an sn of a number sequence (an) is the sum of the sequence members from a1 to an.

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A number sequence is a set of (real) numbers ordered in such a way that it is clear which is the first, second, third … number. One writes for it
(an)={a1; a2; a3 …}
or short
(an)=a1; a2; a3 …
and calls a1, a2, a3 …the members of the number sequence.

Some examples of number sequences are given below.

( 1 ) 1; 5; 9; 13; 17; 21; 25 …

(2) 20; 18; 16; 14; 12; 10 …

(3) 3; 6; 12; 24; 48; 96; 192 …

(4) 1; 12; 14; 18; 116; 132; 164 …

(5) 2; 2; 2; 2; 2; 2; 2 …

(6) 1; -2; 4; -8; 16; -32; 64 …

(7) 1; 4; 9; 16; 25; 36; 49 …

(8) 1; 1; 2; 3; 5; 8; 13 …

Note: Example (8) is the so-called Fibonacci sequence, named after the Italian mathematician LEONARDO FIBONACCI OF PISA (about 1180 to about 1250; Figure 1).

In a number sequence – homework help in algebra , all members are uniquely assigned to the natural numbers. Thus it concerns a function, whose definition range is the set of the natural numbers (or a subset of it beginning with 1) and whose value range is a subset of the real numbers.

A number sequence is called finite if it has only finitely many members – domyhomework.club/accounting-homework/ . However, infinite number sequences are much more interesting, for which it is necessary to specify by a formation rule how the members of the sequence are to be obtained. This can be done either by specifying the n-th (general) member (explicit formation rule) or by describing how the n-th member is formed from the preceding members (recursive formation rule). In the second case, however, the specification of the initial member (or the initial members) is necessary.

In the following table formation rules for the above sequences (1) to (8) are given.

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