If sum of odd terms is A and sum of even terms is B in the expansion x - a n- thenA- A B-1-4x-a2 n-x-a2 nB- 2 A B-x-a2 n-x-a2 n- 4 A B-x-a2 n-x-a2 nD- None of these

The correct option is C (x+a)^n=^nC_0x^n+^nC_1x^n 1a+^nC_2x^n 2a^2+^nC_3x^n 3a^3+⋯ But by the condition, A=^nC_0x^n+^nC_2x^n 2a^2+^nC_4x^n 4a^4+⋯ and B=^nC_1x^ ...

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Byju's Answer

Standard XII

Mathematics

nCr Definitions and Properties

If sum of odd...

Question

If sum of odd terms is A and sum of even terms is B in the expansion $(x + a)^{n}$ , then

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None of these

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Solution

The correct option is C
$(x + a)^{n} =^{n} C_{0} x^{n} +^{n} C_{1} x^{n - 1} a +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{3} x^{n - 3} a^{3} + \dots$
But by the condition,
$A =^{n} C_{0} x^{n} +^{n} C_{2} x^{n - 2} a^{2} +^{n} C_{4} x^{n} - 4 a^{4} + \dots$
$a n d B =^{n} C_{1} x^{n - 1} a +^{n} C_{3} x^{n - 3} a^{3} + \dots$
$H e n c e A B = \frac{1}{4} {(x + a)^{2 n} - (x - a)^{2 n}}$
$O r 4 A B = (x + a)^{2 n} - (x - a)^{2 n}$

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Similar questions

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If sum of odd terms is A and sum of even terms is B in the expansion (x+a)n , then

The correct option is C (x+a)n=nC0xn+nC1xn−1a+nC2xn−2a2+nC3xn−3a3+⋯ But by the condition, A=nC0xn+nC2xn−2a2+nC4xn−4a4+⋯ and B=nC1xn−1a+nC3xn−3a3+⋯ HenceAB=14{(x+a)2n−(x−a)2n} Or 4AB=(x+a)2n−(x−a)2n

If sum of odd terms is A and sum of even terms is B in the expansion $(x + a)^{n}$ , then