Question

34. Find the sum to n terms of the series 5 + 55 + 555 +​

Answer 1

Let S

n

​

=5+55+555+... to n terms.

Then,

s

n

​

=5(1+11+111+... to n terms)

⇒s

n

​

=

5

9

​

(9+99+999+... to n terms)

⇒S

n

​

=

9

5

​

{(10−1)+(10

2

−1)+(10

3

−1)+...+(10

n

−1)}

⇒S

n

​

=

9

5

​

{(10+10

2

+10

3

+...+10

n

)−n}

⇒S

n

​

=

9

5

​

{10(

10−1

10

n

−1

​

)−n}

⇒S

n

​

=

9

5

​

{

9

10

​

(10

n

−1)−n}=

81

5

​

(10

n+1

−9n−10).

Answer 2

Answer:

Answer = 615

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