Question

Use the first three terms of the binomial theorem to approximate 3.56A. 1838.265625B. 1799.75OC. 1761.75OD. 1829.25Reset Selection

Answer 1

Given:

The number to apply binomial theorem.

Required:

Use the first three terms of the binomial theorem to approximate 3.56

Step-by-step explanation:

The binomial theorem is

`(a+b)^n=^nC_0a^nb^0+^nC_1a^(n-1)b^1+^nC_0a^(n-2)b^2+\cdot\cdot\cdot\cdot\cdot`

Now, first three terms approximation

`\begin{gathered} (3+0.5)^6=^6C_0*3^6*0.5^0+^6C_1*3^5*0.5^1+^6C_2*3^4*0.5^2 \\ =729+729+303.75 \\ =1761.75 \end{gathered}`

Answer:

Option C is correct.