Question

Find the sum of the series​

Answer 1

Answer:

Step-by-step explanation:

S = 0.3+0.33+0.333+……n terms.

Now taking 3 common from the sum we have ,

S = 3 x [0.1+0.11+0.111+…. n terms]

Now to further simplify , we can multiply and divide by 9,

S = 3/9 x [0.9+0.99+0.999+…..n terms]

We can also write this as,

S = 3/9 x [(1–0.1)+(1–0.01)+(1–0.001)+……n terms]

Summing up all the 1’s, it becomes n times ,

S = 1/3 x [n - (0.1 + 0.01 + 0.001 +….. n terms)]

Applying the G.P formula ,

S = 1/3 x (n – 0.1[1 - (0.1)^n]/1 – 0.1)

S = 1/3 x (9n – {1 – [0.1]^n}/9)

Hope This Helps You