Write down the first three terms in ascending powers of $x$ of the expansion of \({{\left( 1-x \ri

Question

Write down the first three terms in ascending powers of $x$ of the expansion of ${{\left( 1-x \right)}^{-2}}$. State the coefficient of ${{x}^{n}}$ and the range of values of $x$ for which the expansion is valid. Hence, or otherwise, find the value of $\sum_{n=1}^{\infty} \frac{n}{2^n}$.[5]

Accepted Answer

First 3 terms: $1 + 2x + 3x^2$; Coefficient of $x^n$: $n + 1$; Range: $-1 < x < 1$; $2$

2008 YJC P1 Q3

2008 YJC P1 Q3

Video Solution:

Solution:

Solution locked