The sum here, however, is not used in the traditional sense. Surprisingly, the sum has been proved to converge to -1/12. Interesting fact: The Ramanujan Summation is the sum of all natural numbers starting from 1 to infinity. You will come across a number of series including the famous Taylor’s series, Binomial series etc. Series have profound applications in many areas of study in mathematics (both finite and infinite series), physics, finance, computer science etc. Quick Quiz: Is the series 1+1/2+1/3+1/4… convergent or divergent? An example of divergent series is 2+4+8…. If the sum of elements of infinite series does not converge to a real number, the series is said to be a divergent series. One of the well-known convergent series is 1/2+1/4+1/8… which sums up to 1. If the sum of elements of infinite series ‘converges’ to a real number, the series is said to be a convergent series. Second, the infinite series can be a Convergent or a Divergent series. First, since series is a sum, therefore, the order of elements does not matter! (as opposed to a sequence). Series bring forth some exciting aspects. The above given series is an example of an infinite series. Like there are finite/infinite sequences, there are also finite/infinite series. Interestingly, the sequences D, R, A, W, E, R and R, E, W, A, R, D are two entirely different sequences.It should be remembered that the Rule can be anything that defines the ‘ nature’ of the sequence. Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune is a sequence of planets in solar system with respect to distance from the Sun.1, 3, 5, 7, 9 is a sequence of first five positive odd numbers.a, b, c, d, …., x, y, z is a sequence of all alphabets from a to z.Let us have a look at some examples (The respective Rule is bold). The things to remember include, a Rule that defines the relation between objects, the order in which the objects are mentioned and the fact that repetition is allowed. The sequence (or progression) is a list of objects, usually numbers, that are ordered and are bounded by a rule. The teacher told her that we she had ‘discovered’ is called a ‘Sequence’ in basic Arithmetic. Mary wrote the numbers, in order, on a paper and showed it to her teacher. She jotted down the height attained by the ball in each successive bounce. Young Mary was observing the motion of a rubber ball as she dropped it on a floor.
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