If the expansion in powers of x of the function 1/(1-ax)(1-bx) is a_0 + a_1x + a_2x^2 + a_3x^3 + , then a_n is: - Mathematics MCQ AIEEE 2006 2026 | ExamTest.live

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If the expansion in powers of x of the function \frac{1}{( 1 - a x ) ( 1 - b x )} is a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots, then a_{n} is:

Solution & Step-by-step Explanation

Using partial fractions: Expand using the geometric series : The coefficient of , denoted as , is:

Try it yourself before checking the explanation above.

If the expansion in powers of x of the function \frac{1}{( 1 - a x ) ( 1 - b x )} is a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + \dots, then a_{n} is:

\frac{b ^{n} - a ^{n}}{b - a}

\frac{a ^{n} - b ^{n}}{b - a}

\frac{a ^{n + 1} - b ^{n + 1}}{b - a}

\frac{b ^{n + 1} - a ^{n + 1}}{b - a}

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