engineering recuitment GATE CSE 2023-24 Test Series Engineering Mathematics Combinatorics Generating Functions
Which is the closed form of expression an = an-1 + 2n where a0 = 2 for all n = 0, 1, 2, 3, …?
1
\(G\left( x \right) = \frac{2}{{1 - x\;}} + \frac{{2x}}{{{{\left( {1 - x} \right)}^2}}}\)
2
\(G\left( x \right) = \frac{2}{{1 - x\;}} + \frac{{2x}}{{{{\left( {1 - x} \right)}^3}}}\)
3
\(G\left( x \right) = \frac{2}{{1 - x\;}} + \frac{{4x}}{{{{\left( {1 - x} \right)}^3}}}\)
4
\(G\left( x \right) = \frac{2}{{1 - x\;}} + \frac{x}{{{{\left( {1 - x} \right)}^3}}}\)