a word problem requiring either factorials or binomial expansions to solve
in Algebra 2 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

PROBLEM: Given the fact that seven tenths is approximately equal to the square root of a half, use a binomial expansion to produce an infinite series converging to the square root of two.


7/10≃√½, then 10/7≃√2 and (10/7)²=100/49. But 100/49-2/49=98/49=2.

Therefore, √(100/49-2/49)=√2, and 100/49-2/49 can be written (100/49)(1-0.02) and the square root can be written: (10/7)√(1-0.02) or (10/7)(1-0.02)^½.

Now we can expand the binomial:


We now have an infinite series for √2.


By simply changing 10/7 to 5/7 we get a series for √½, because √½=√2/2. By changing 10/7 to 20/7 we get a series for √8, and so on for other multiples.

by Top Rated User (781k points)

Related questions

0 answers
asked Nov 12, 2011 in Statistics Answers by anonymous | 609 views
1 answer
1 answer
1 answer
asked Jul 9, 2019 in Other Math Topics by anonymous | 109 views
Welcome to MathHomeworkAnswers.org, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
85,299 questions
90,692 answers
98,429 users