find the sum of the following sequence to n terms 9,99,999,9999.......
Answers
Answered by
1
Answer:11106
Step-by-step explanation:
9+99+999+9999 = 11106
Answered by
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 )
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