Question

Find the sum of infinity 9+3+1....​

Answer 1

Answer:

13

Step-by-step explanation:

I hope my answer helps you dear

Answer 2

Answer:-

Given:

9 + 3 + 1..... ∞ are in GP.

Here,

• a = 9
• r = 3/9 = 1/3

We know that,

Sum of an infinite GP (S∞) = a/1 - r

So,

⟶ S∞ = 9/ (1 - 1/3)

⟶ S∞ = 9 / (3 - 1 / 3)

⟶ S∞ = 9 * 3/2

⟶ S∞ = 27/2

∴ The sum of the given GP is 27/2.

Additional Information :-

• A sequence (finite or infinite) on non - zero numbers in every term except the first term , bears a constant ratio with its receding term is called a Geometric progression (GP).

• General form of a GP is a , ar , ar² .... a × rⁿ⁻¹

• The nth term from the end of a GP with the last term l and common ratio r is 1/rⁿ⁻¹

• Sum of first n terms of a GP = a(rⁿ - 1) / r - 1 (r ≠ 1 & n is finite)

• Sum of first n terms of a GP = a × n (r = 1 & n is finite)

• Sum of first n terms of a GP = a/1 - r ( | r | < 1 & n ⟶ ∞ )