JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

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Application +4 | -1

Let

S_1, S_2, \ldots

be squares such that for each

n \geq 1

, the length of a side of

S_n

equals the length of the diagonal of

S_{n+1}

. If the length of a side of

S_1

10 \mathrm{~cm}

and the area of

S_n

less than

1 \mathrm{sq} \mathrm{cm}

, then the least value of

n

View answer and explanation

Correct option: B

Option B (8) is correct because the area of the nth square must be less than 1, which leads to the inequality

2^{n-1} > 100

, and the smallest integer n that satisfies this is 8.

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