How to solve:- binomial expansion (1+2x)^1/2

Welcome to my article binomial expansion (1+2x)^1/2. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question binomial expansion (1+2x)^1/2, read and understand it carefully till the end.

Let us know how to solve this question binomial expansion (1+2x)^1/2.

First write the question on the page of the notebook.

binomial expansion (1+2x)^1/2

According to dinomeat series-

latex \displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+\frac{{2x}}{2}+\frac{{\left( {\frac{1}{2}} \right)\left( {\frac{1}{2}-1} \right)}}{{2!}}{{(2x)}^{2}}+\frac{{\left( {\frac{1}{2}} \right)\left( {\frac{1}{2}-1} \right)\left( {\frac{1}{2}-2} \right)}}{{3!}}{{(2x)}^{3}}+\frac{{\left( {\frac{1}{2}} \right)\left( {\frac{1}{2}-1} \right)\left( {\frac{1}{2}-2} \right)\left( {\frac{1}{2}-3} \right)}}{{4!}}{{(2x)}^{4}}+\text{.................................}.

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x+\frac{{\left( {\frac{1}{2}} \right)\left( {-\frac{1}{2}} \right)}}{{2!}}4{{x}^{2}}+\frac{{\left( {\frac{1}{2}} \right)\left( {-\frac{1}{2}} \right)\left( {-\frac{3}{2}} \right)}}{{3!}}8{{x}^{3}}+\frac{{\left( {\frac{1}{2}} \right)\left( {-\frac{1}{2}} \right)\left( {-\frac{3}{2}} \right)\left( {-\frac{5}{2}} \right)}}{{4!}}16{{x}^{4}}+…………….

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{1}{8}4{{x}^{2}}+\frac{3}{{48}}8{{x}^{3}}-\frac{{15}}{{384}}16{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{{1\times 4{{x}^{2}}}}{8}+\frac{{3\times 8{{x}^{3}}}}{{48}}-\frac{{15\times 16{{x}^{4}}}}{{384}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{{4{{x}^{2}}}}{8}+\frac{{24{{x}^{3}}}}{{48}}-\frac{{15\times 16{{x}^{4}}}}{{384}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{{4{{x}^{2}}}}{8}+\frac{{24{{x}^{3}}}}{{48}}-\frac{{15\times 16{{x}^{4}}}}{{24\times 16}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{4}{8}{{x}^{2}}+\frac{{24}}{{48}}{{x}^{3}}-\frac{{15\times 16}}{{24\times 16}}{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{{4\times 1}}{{4\times 2}}{{x}^{2}}+\frac{{24\times 1}}{{24\times 2}}{{x}^{3}}-\frac{{16\times 15}}{{16\times 24}}{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{{4\times 1}}{{4\times 2}}{{x}^{2}}+\frac{{24\times 1}}{{24\times 2}}{{x}^{3}}-\frac{{16\times 15}}{{16\times 24}}{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{1}{2}{{x}^{2}}+\frac{1}{2}{{x}^{3}}-\frac{{15}}{{24}}{{x}^{4}}+……..]

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{1}{2}{{x}^{2}}+\frac{1}{2}{{x}^{3}}-\frac{{3\times 5}}{{3\times 8}}{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{1}{2}{{x}^{2}}+\frac{1}{2}{{x}^{3}}-\frac{5}{8}{{x}^{4}}+……..

\displaystyle {{\left( {1+2x} \right)}^{{\frac{1}{2}}}}=1+x-\frac{1}{2}{{x}^{2}}+\frac{1}{2}{{x}^{3}}-\frac{5}{8}{{x}^{4}}+……..[Answer]

mathwaycalulus.com

This article binomial expansion (1+2x)^1/2 has been completely solved by tireless effort from our side, still if any error remains in it then definitely write us your opinion in the comment box. If you like or understand the methods of solving all the questions in this article, then send it to your friends who are in need.

See also  How to solve 25 cm to inches ?

Note: If you have any such question, then definitely send it by writing in our comment box to get the answer.
Your question will be answered from our side.
Thank you once again from our side for reading or understanding this article completely.

Leave a Comment