Question

find the sum of GP of the following series 5 , 5 5 , 5 5 5 and so on​

Answer 1

Step-by-step explanation:

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

Then,

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

⇒sn =59 (9+99+999+... to n terms)

⇒Sn = 95 {(10−1)+(10 2−1)+(10 3 −1)+...+(10 n −1)}

⇒Sn= 95 {(10+10 2+10 3+...+10n)−n}

⇒Sn = 95{10( 10−110 n −1 )−n}

⇒Sn= 95{ 910(10 n−1)−n}

= 815(10 n+1−9n−10).