Question

if (1+x^3)^0.6= sigma (n=0 to infinity) bn x^n then b3=?

Answer 1

\[(1 + x ^{3})^{0.6} = \sum_{n=0}^{\infty} b_{n}x ^{n}\]

Answer 2

think of taylor series for \( f(x)=(1+x^3)^{0.6} \) in neighborhood of 0 then u have

\[ f(x)=(1+x^3)^{0.6}=\sum_{n=0}^{\infty} \frac{f^n(x)}{n!} x^n \] so find \(b_3\) Using
\[ b_n=\frac{f^n(x)}{n!} \]