NCERT Book Class 11 Maths Infinite Series

As discussed in the Chapter 9 on Sequences and Series, a sequence a₁, a₂, ..., a_n, ... having infinite number of terms is called infinite sequence and its indicated sum, i.e., a₁ + a₂ + a₃ + ... + an + ... is called an infinte series associated with infinite sequence. This series can also be expressed in abbreviated form using the sigma notation, i.e.,

In this Chapter, we shall study about some special types of series which may be required in different problem situations. A.1.2 Binomial Theorem for any Index
In Chapter 8, we discussed the Binomial Theorem in which the index was a positive integer. In this Section, we state a more general form of the theorem in which the index is not necessarily a whole number. It gives us a particular type of infinite series, called Binomial Series. We illustrate few applications, by examples. We know the formula


 n is non-negative integer. Observe that if we replace index n by negative integer or a fraction, then the combinations C n r do not make any sense. We now state (without proof), the Binomial Theorem, giving an infinite series in which the index is negative or a fraction and not a whole number. Theorem The formula

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