Question

13. 2 + 22 + 222 +
A) og [10 (10^-1) - 9n] B) 110 (10"-1)- 9n]
C D), [1 - (0.1)1
C) = [1 - (0.1)"]
C​

Answer 1

Answer:

S=2+22+222+...nterms

S=  

9

2

​  

(9+99+999+....nterms)

S=  

9

2

​  

((10−1)+(10  

2

−1)+(10  

3

−1)+...nterms)

S=  

9

2

​  

(10+10  

2

+....+10  

n

−n)

S=  

9

2

​  

(  

9

10  

n+1

−1

​  

−1−n)

=  

9

2

​  

(  

9

10  

n+1

−10

​  

−n)

S=  

81

2

​  

(10  

n+1

−9n−10)

Step-by-step explanation: