JEE MATHEMATICS MCQ: SEQUENCE OF SERIES

1 Hard

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Application +4 | -1

Let

{S_1},\;{S_2}, \ldots

be squares such that for each

n \ge 1,

the length of a side of

{S_n}

equals the length of a diagonal of

{S_{n + 1}}.

If the length of a side of

{S_1}

is 10cm, then for which of the following values of

n

is the area of

{S_n}

less than 1 sq cm?

View answer and explanation

Correct option: C

Option C (9) is correct because after determining the side length of successive squares, the area of S_n becomes less than 1 sq cm when n = 9.

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