Difference between revisions of "1962 AHSME Problems/Problem 40"
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<math>\frac{1}{10}+\frac{0.2}{10}+\frac{0.03}{10}+\frac{0.004}{10}</math>. | <math>\frac{1}{10}+\frac{0.2}{10}+\frac{0.03}{10}+\frac{0.004}{10}</math>. | ||
Now, it is trivial that the new fraction we seek is <math>\frac{1.234567891011......}{10}</math> | Now, it is trivial that the new fraction we seek is <math>\frac{1.234567891011......}{10}</math> | ||
− | + | ||
+ | Testing the answer choices, we see that <math>\boxed{B}</math> is the correct answer. |
Revision as of 22:03, 24 July 2017
Problem
The limiting sum of the infinite series, whose
th term is
is:
Solution
The series can be written as the following:
and so on.
by using the formula for infinite geometric series ,
We can get
...
Since they all have common denominators, we get
.
Using the infinite series formula again, we get
Solution 2
So.. we have the sum to be ...
Notice that this can be written as
.
Now, it is trivial that the new fraction we seek is
Testing the answer choices, we see that is the correct answer.