AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Let S₁ , S₂ ..... be the squares such that for each n $\geq$ 1 the length of side S_n is equal to length of the diagonal of S_n+1 . If the length of the side of S₁ is 10 cm, the least value of ‘n’ for which area of S_n < 1 sq.cm is_____

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Side of the Square S₁= 10cm

$Diagonal of a Square S_{2} = 10 \sqrt{2} ss$

$Side of the Square S_{2} = \frac{10}{\sqrt{2}} cm$

$Similarly side of the square S_{3} = \frac{10}{(\sqrt{2})^{2}} cm$

$Side of the square S_{n} = \frac{10}{(\sqrt{2})^{n - 1}}$

But area of $S n < 1 \Rightarrow {(\frac{10}{(\sqrt{2})^{n - 1}})}^{2} < 1$

$\Rightarrow 100 < 2^{n - 1}$

Watch 3-min video & get full concept clarity

courses

No courses found

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!