Question

find the sum of the following sequence to n terms 9,99,999,9999.......​

Answer 1

Answer:11106

Step-by-step explanation:

9+99+999+9999 = 11106

Answer 2

Answer:

( 10 * ( 10 ^ n - 1 ) - ( 9 * n ) / 9 )

Step-by-step explanation:

Well first we have to convert it into easier form :

10 ^ 1 - 1 , 10 ^ 2 - 1 , 10 ^ 3 - 1 , 10 ^ 4 - 1 , ... , 10 ^ n - 1

The sum of it would be ( 10 ^ 1 - 1 + 10 ^ 2 - 1 + 10 ^ 3 - 1 + 10 ^ 4 - 1 + ... )

= ( 10 ^ 1 + 10 ^ 2 + 10 ^ 3 + 10 ^ 4 + ... + 10 ^ n ) - ( n * 1 )

= ( 10 * ( 10 ^ n - 1 ) / 10 - 1 ) - n

= ( 10 * ( 10 ^ n - 1 ) - ( 9 * n ) / 9 )