JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Analyzing +4 | -1

Let

A_{n}=\left(\frac{3}{4}\right)-\left(\frac{3}{4}\right)^{2}+\left(\frac{3}{4}\right)^{3}-\ldots+(-1)^{n-1}\left(\frac{3}{4}\right)^{n}

and

B_{n}=1-A_{n}

. Then, the least odd natural number

p

, so that

B_{n}>A_{n}

, for all

n \geq p

View answer and explanation

Correct option: C

Option C (11) is correct because by analyzing the inequality

B_n > A_n

and using the G.P. formula, we find that the least odd natural number p satisfying the condition is 11.

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