Binomial theorem facilitates the algebraic expansion of the binomial (a + b) for a positive integral exponent n.

**Introduction**

Binomial theorem
facilitates the algebraic expansion of the binomial (*a*
+ *b*) for a positive integral exponent *n*. Binomial theorem is used in all branches of Mathematics and
also in other Sciences. Using the theorem, for example one can easily find the
coefficient of *x*^{20} in the expansion of (2*x−*7)^{23}*.* If one wants to know
the maturity amount after 10 years on a sum of money deposited in a
nationalised bank at the rate of 8% compound interest per year or to know the size of population of
our country after 15 years if the annual growth rate and present population
size are known, Binomial theorem helps us in finding the above quantities. The
coefficients that appear in the binomial expansion of (*a* + *b*)* ^{n}*,

Greek Mathematician
Euclid mentioned the special case of binomial theorem for exponent 2*.*
Binomial theorem for exponent 3 was known by 6* ^{th}* century in India. In
1544, Michael Stifel (German Mathematician) introduced the term

Over the period of
thousand years, legends have developed mathematical problems involving
sequences and series. One of the famous legends about series concerns the
invention of chess, where the cells of chess board were related to 1*,*
2*,*
4*,*
8*, . . .* (imagine the number related to 64* ^{th}* cell). There are many
applications of arithmetic and geometric progressions to real life situations.

In the earlier classes
we have learnt about sequences, series. Roughly speaking a sequence is an arrangement
of objects in some order and a series is the sum of the terms of a sequence of
numbers. The concept of infinite series helps us to compute many values, like sin 9/44 *π*, log 43 and *e*^{20} to a desired level of
approximation. Sequences are important in differential equations and analysis.
We learn more about sequences and series.

Tags : Mathematics , 11th Mathematics : UNIT 5 : Binomial Theorem, Sequences and Series

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11th Mathematics : UNIT 5 : Binomial Theorem, Sequences and Series : Binomial Theorem, Sequences and Series: Introduction | Mathematics

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