Binomial Theorem Questions (605)

\(1 + \dfrac{1}{3}x + \dfrac{1 \times 4}{3 \times 6}x^2 + \dfrac{1 \times 4 \times 7}{3 \times 6 \times 9}x^3 + \cdots\) is equal to

Find the number of nonzero terms in the expansion of \((1 + 3\sqrt{2}\,x)^9 + (1 - 3\sqrt{2}\,x)^9\).

\({}^{40}C_4 + {}^4C_1 \cdot {}^{303}C_4 + {}^4C_2 \cdot {}^{202}C_4 - {}^4C_3 \cdot {}^{101}C_4\) is equal to

Find the value of \(\{3^{2003}/28\}\), where \(\{\cdot\}\) denotes the fractional part.

The sum of coefficients of integral powers of \(x\) in the binomial expansion of \((1 - 2\sqrt{x})^{50}\) is