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The geometric series you have is equivalent to evaluating 1 1 − x at x = 2; the − 1 is valid for that formula, but you are using the series outside its region of validity, which is where the trouble lies. That should beg the question of why adding up a bunch of positives results in a negative... ;) – J. M. ain't a mathematician.
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Stack Exchange Network. Stack Exchange network consists of...
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Sequences and Series Cheat Sheet. sequence is a list of terms. For example, 3, 6, 9, 12, 15, ... series is the sum of a list of terms. For example, 3 + 6 + 9 + 12 + 15 + ... The terms of a sequence are separated by a comma, while with a series they are all added together.
The series of numbers 1, 2, 4, 8, 16 ... is an example of a geometric sequence, sometimes called a geometric progression (GP). Each term in the progression is found by multiplying the previous number by 2. Such sequences occur in many situations; the multiplying factor does not have to be 2.
Learn how to solve 1,2,4,8,16. Tiger Algebra's step-by-step solution shows you how to find the common ratio, sum, general form, and nth term of a geometric sequence.
The series of numbers 1, 2, 4, 8, 16 ... is an example of a geometric sequence, sometimes called a geometric progression (GP). Each term in the progression is found by multiplying the previous number by 2. Such sequences occur in many situations; the multiplying factor does not have to be 2.
SYNOPSIS. Kings should be treated courteously! At least, that’s what famous music critic Georg (Josef Hader) thinks. But he finds himself counting pennies when his chief editor (Jörg Hartmann) sud-denly fires him from the Viennese newspaper for which he has been writing for decades.
A series is the sum of the terms of a sequence. For example, the harmonic series is 1+ 1 2 + 1 3 + 1 4 +··· and the alternating harmonic series is 1− 1 2 + 1 3 − 1 4 +··· The summation notation If we consider a general sequence a 1, a 2, ..., a n, ... then the sum of the first k terms a 1 +a 2 +a 3 +···+a k is concisely denoted by ...
