SOLUTION: Which series has a sum? A. 1-2+4-8+... B. 1+3+5+7+... C. -1+1-1+1-... D. 0.1+0.2+0.3+0.4+... E. 0.21+0.0021+0.000021+...

Algebra ->  Sequences-and-series -> SOLUTION: Which series has a sum? A. 1-2+4-8+... B. 1+3+5+7+... C. -1+1-1+1-... D. 0.1+0.2+0.3+0.4+... E. 0.21+0.0021+0.000021+...      Log On


   

Question 82383This question is from textbook
: Which series has a sum?
A. 1-2+4-8+...
B. 1+3+5+7+...
C. -1+1-1+1-...
D. 0.1+0.2+0.3+0.4+...
E. 0.21+0.0021+0.000021+... This question is from textbook

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
0.21+0.0021+0.000021+...
This is a repeating decimal so it is a rational number.
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Adding the terms you would get 0.2121212121....
Let x= 0.212121212...
Then 100x = 21.2121212121...
Subtract the 1st equation from the 2nd to ge:
99x= 21
Then x=21/99
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Cheers,
Stan H.