According to the use of binomial expansion, the approximate value of √3 is found by applying the infinite sum √3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...

An acceptable result cannot be found manually for it requires a high number of elements, with the help of a solver we find that the approximate value of √3 is 1.732.

<h3>How to approximate the value of a irrational number by binomial theorem</h3>

Binomial theorem offers a formula to find the analytical form of the power of a binomial of the form (a + b)ⁿ:

$(a + b)^{n} = \sum \limits_{k = 0}^{n} \left(\begin{array}{c}n\\k\end{array}\right)\cdot a^{n-k} \cdot b^{k}$ (1)

Where:

a, b - Constants of the binomial.
n - Grade of the power binomial.
k - Index of the k-th element of the power binomial.

If we know that a = 1, b = 2 and n = 1 / 2, then an approximate expression for the square root is:

√3 = 1 + (1 /2) · 2 - (1 / 8) · 2² + (1 / 16) · 2³ - (5 / 128) · 2⁴ + (7 / 256) · 2⁵ - (21 / 1024) · 2⁶ + (33 / 2048) · 2⁷ - (429 / 32768) · 2⁸ +...

To learn more on binomial expansions: brainly.com/question/12249986

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8 0

1 year ago

9x + 26 + 7x - 17 = 2x + (-3x) + 5x 16x + 9 = 0 16x + 11 = 4x 16x + 9 = 4x

zzz [600]

Answer:

C. 16x+9=4x

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Write an expression that is equivalent to 3/5 (3y+15) 3/5y +9, 3/5y+15, 9/5y+9, 9/5y + 15?

NISA [10]

Given the expression

$\frac{3}{5} (3y+15)$

The expression that is equivalent to the given expression is given by:

$\frac{3}{5} (3y+15)= \frac{9}{5} y+ \frac{3}{5} (15)= \frac{9}{5} y+9$

6 0

3 years ago