SOLUTION: Find the sum of the following sequence : 2, 22, 222, ......... to n terms.

Question 1088866: Find the sum of the following sequence :
2, 22, 222, ......... to n terms.
Answer by ikleyn(52781) (Show Source): You can put this solution on YOUR website!
.

Let  = 2 + 22 + 222 + . . . + the last n-th term.


Then  = 9 + 99 + 999 + . . . + the last term written with n "9".


The k-th term plus 1 is equal to .  Therefore,

 =  - .


Next, apply the formula for the sum of geometric progression .

On geometric progressions, see the introductory lessons
    - Geometric progressions
    - The proofs of the formulas for geometric progressions
    - Problems on geometric progressions
    - Word problems on geometric progressions
in this site.

Also, you have this free of charge online textbook in ALGEBRA-II in this site
    - ALGEBRA-II - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic
"Geometric progressions".

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