defence exam Agniveer Vayu Group X & XY Mock Test 01/2026 Mathematics Binomial Theorem Binomial Expansion
If the expansion of powers of x of the function \(\frac{1}{{(1 - ax)\,(1 - bx)}}\) is \(\,{a_0} + {a_1}x + {a_2}{x^2} + {a_3}{x^3}\) + _____, then an is
1
\(\frac{{{b^n} - {a^n}}}{{b - a}}\)
2
\(\frac{{{a^n} - {b^n}}}{{b - a}}\,\)
3
\(\frac{{{a^{n + 1}} - {b^{n + 1}}}}{{b - a}}\,\)
4
\(\frac{{{b^{n + 1}} - {a^{n + 1}}}}{{b - a}}\,\)