Question

Explain why it would not make sense to approximate 256 using the binomial theorem for the binomial (20 5)6.

Answer 1

It would not make sense to approximate 256 using the binomial theorem for the binomial (20 5)6 because 5  is outside of the range of -1 and 1, it will not go close to 0 when multiplied by a positive integer exponent.

What do you mean by binomial theorem?

According to the binomial theorem, the nth power of the sum of two positive integers a and b can be written as the sum of the components in the form n + 1. Triangle of Yang Hui Al-Karaj, Bernhard Bolzano are significant figures. Algebraic subjects are related. The binomial triangle coefficient of Pascal.

According to the given information:

The Binomial Theorem with a power of 6 is expressed as follows:

$(x+y)^{6}=x^{6}+6 x^{5} y+15 x^{4} y^{2}+20 x^{3} y^{3}+15 x^{2} y^{4}+6 x y^{5}+y^{6}$

Thus, if we substitute 20 for x and 5 for y, our first term will be 20^6 = 64000000, which is significantly larger than 256, and it will be pointless to utilize the binomial theorem to(20 +5 )^6 approximate 256 in this case.

Furthermore, since that has no power and the Binomial Theorem utilizes power, using (20 +5 )^6 it makes no sense.

(20 +5 )^6 = 150 ≠ 256

Since 5 is outside of the range of -1 and 1, it will not go close to 0 when multiplied by a positive integer exponent.

To know more about binomial Theorem visit:

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