Question

9)
Find the nth term of the sequence
0.6,0.66,0.666,0.6666, ...​

Answer 1

Step-by-step explanation:

Given : Series 0.6+0.66+0.666+0.6666

To find :The sum of series up-to n terms

Solution :

Let  denotes the sum of n terms.

Sum of (1+1+1+1.....1) n times = n

Apply G.P series in second bracket in which

Sum of G.P series is

Therefore, The sum of series of n terms is given by,

S_n=\frac{6}{9}[n-\frac{1}{9}(1-\frac{1}{10^n})]

Answer 2

Answer:

2/3[1-(0.1)n]

Step-by-step explanation:

0.6,0.66,0.666,0.6666....................

=6(0.1 , 0.01 , 0.001...................). Remove common

Multiply and divide with 9

=6/9(0.9 , 0.09 ,0.009..................)

To get 0.9 subtract with 0.1-1

=6/9(1-0.1 , 1-0.01 , 1-0.001...............)

Taking positive at one side and negative at one side

=6/9(1+1+1+1+1...................-0.1-0.01-0.001)

=6/9[1-(0.1)n]

=2/3[1-(0.1)n]