Maharashtra State Board 11th Maths Solutions Chapter 2 Sequences and Series Ex 2.3
Solution & Step-by-Step Answer:
(ii)
Solution:
(iii)
Solution:
(iv)
Solution:
(v) 9, 8.1, 7.29, ……
Solution:
9, 8.1, 7.29, …..
Here, a = 9, r = = 0.9, |r| < 1
∴ Sum to infinity exists.
∴ Sum to infinity =
=
=
= 90
Solution & Step-by-Step Answer:
(i) = 0.7777… = 0.7 + 0.07 + 0.007 + …. The terms 0.7, 0.07, 0.007,… are in G.P. ∴ a = 0.7, r = = 0.1, |r| = |0.1| < 1 ∴ Sum to infinity exists. ∴ Sum to infinity
(ii) = 2.444 … = 2 + 0.4 + 0.04 + 0.004 + …
The terms 0.4, 0.04, 0.004,… are in G.P.
∴ a = 0.4, r = = 0.1, |r| = 10.11 < 1
∴ Sum to infinity exists.
∴ Sum to infinity
(iii) = 2.3555… = 2.3 + 0.05 + 0.005 + 0.0005 + …
The terms 0.05,0.005,0.0005,… are in G.P.
∴ a = 0.05, r = = 0.1, |r| = |0.1| < 1
∴ Sum to infinity exists.
∴ Sum to infinity
(iv) = 51.0222 …. = 51 + 0.02 + 0.002 + 0.0002 + …..
The terms 0.02, 0.002, 0.0002,… are in G.P.
∴ a = 0.02, r = = 0.1, |r| = |0.1| < 1
∴ Sum to infinity exists.
∴ Sum to infinity
Solution & Step-by-Step Answer:
r = , sum to infinity = 12 ….. [Given] Sum to infinity = 12 = a = 12 × ∴ a = 4
Solution & Step-by-Step Answer:
a = 6, sum to infinity = …..[Given] Sum to infinity =
Solution & Step-by-Step Answer:
Let the required G.P. be a, ar, ar2, ar3, ….. Sum to infinity of this G.P. = 5
Solution & Step-by-Step Answer:
(ii)
Solution:
(iii)
Solution:
(iv)
Solution:
Solution & Step-by-Step Answer:
(i) Area of the 1st square = 12 Area of the 2nd square = Area of the 3rd square = and so on. ∴ Sum of the areas of all the squares ∴ Sum to infinity exists. ∴ Sum of the areas of all the squares = = 2
(ii) Perimeter of 1st square = 4
Perimeter of 2nd square = 4
Perimeter of 3rd square = 4
and so on.
Sum of the perimeters of all the squares
Solution & Step-by-Step Answer:
Here, on the first bounce, the ball will go 6 m and it will return 6 m. On the second bounce, the ball will go 3.6 m and it will return 3.6 m, and so on. Given that, a ball is dropped from a height of 10 m. ∴ Total distance travelled by the ball is = 10 + 2[6 + 3.6 + …] The terms 6, 3.6 … are in G.P. a = 6, r = 0.6, |r| = |0.6| < 1 ∴ Sum to infinity exists. ∴ Total distance travelled by the ball
