30) A circle C1 is inscribed in a square S1 of side a1 Another square S2 of side a2 - Maths -

Question

30) A circle C1 is inscribed in a square
S1 of side a1 Another square S2 of
side a2 is inscribed C1 A circle
C2 is inscribed in S1 The process is
continued if a1 = 4 √2, and s =
a1 + a2 + … ∞
then ( √2 – 1)s = ___

Anuradha Sharma · Accepted Answer

Hi,
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ana_qa_image_58fb90a03335c%20png">

side of square will be diameter of circle 1 and then this diameter will act as diagonal for second square so a1= a22a2= a12similarlya3= 12×a12a4= 12×12×a12
so a1+a2+a3+
∞= a1+ a12+12×a12+12×12×a12+
it is infinite GP  with first term a = a1 and r = 12so s=a11-12= 2×422-12-1s= 8

30) A circle C1 is inscribed in a square S1 of side a1. Another square S2 of side a2 is inscribed C1. A circle C2 is inscribed in S1. The process is continued.. if a1 = 4 √2, and s = a1 + a2 + ….. ∞ then ( √2 – 1)s = ___

30) A circle C₁ is inscribed in a square S₁ of side a₁. Another square S₂ of side a₂ is inscribed C₁. A circle C₂ is inscribed in S₁. The process is continued.. if a₁ = 4 √2, and s = a₁ + a₂ + ….. ∞ then ( √2 – 1)s = ___