Firstly, write the expression as $\left(1+2x\right)^{-2}$. For all complex values of , and non-negative integer values of r , s , the Pascal's formula ( r ) + ( r + 1 ) = ( + 1 r + 1 ) Report. A binomial contains exactly two terms. Finally, by setting $x=0.1$, we can find an approximation to $\sqrt{3.7}$: $\left(3.7\right)^{\frac{1}{2}}\approx 2-\frac{3}{4}\times 0.1-\frac{9}{64}\times 0.1^2\approx 1.9246 $. Convergence at the limit points 1 is not addressed by the present analysis, and depends upon m . We can then find the expansion by setting $n=-2$ and replacing all $x$ with $2x$: $\begin{array}{l}&&\left(1+2x\right)^{-2}\\&=&1-2(2x)+\frac{-2(-3)}{1\times 2}(2x)^2+\frac{-2(-3)(-4)}{1\times 2\times 3}(2x)^3+\\&=&1-4x+12x^2-32x^3+\end{array}$. Here are the steps to do that. Step 3. As the name suggests, when binomial expressions are raised to a power or degree, they have to be expanded and simplified by calculations. State the range of values of $x$ for which this approximation is valid. Let us start with an exponent of 0 and build upwards. Since the power is 3, we use the 4th row of Pascal's triangle to find the coefficients: 1, 3, 3 and 1. Indeed (n r) only makes sense in this case. quite confusing written in this form haha 0 reply Theloniouss Universities Forum Helper Badges: 21 Rep: ? \(\left(\frac{n}{2}+1\right)\)th term is the middle term. Moreover, the coefficient of y is equal to 1 and the exponent of y is 1 and 9 is the constant in the equation. We reduce the power of (2) as we move to the next term in the binomial expansion. According to the binomial expansion theorem, it is possible to expand any power of x + y into a sum of the terms. For , the negative binomial series simplifies to. The first expansion is valid for $\vert -x\vert <1$ (or $-1 Cheap Restaurant With Eiffel Tower View,
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