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

The length of a side of a square is ‘a’ meter. A second square is formed by joining the middle points of this square. Then a third square is formed by joining the middle points of the second square and so on. Then the sum of the area of the squire which carried up to infinity 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

a^{2}

2 a^{2}

3 a^{2}

4 a^{2}

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

Given side of square =

a

The area of square side a =

a^{2}

The side of the square formed by joining the midpoints of original square=

\frac{a}{\sqrt{2}}

Similarly, the second area square =

\frac{a^{2}}{2}

Also, the area of third square which is formed in the same way =

\frac{a^{2}}{2}

Here, we get,
Sides are

a,

\frac{a}{\sqrt{2}}, \frac{a}{2}, \frac{a}{2 \sqrt{2}}

Also, the area of these sides,

a^{2}, \frac{a^{2}}{2}, \frac{a^{2}}{4}, \frac{a^{2}}{8}

Here, the sum of areas of each of those squares is an infinite geometric series in which
First term a= a2 Common ratio r= 1/2
So, the sum of this series,

S_{\infty} = \frac{a}{1 - r}

= \frac{a^{2}}{(1 - \frac{1}{2})}

= 2 a^{2}

So, the required sum is

2 a^{2} .

Hence, option 2 is correct.

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!