?How do you find the sum of the infinite geometric series 343+49+7+...?

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Answer 1 · 2015-11-17T10:56:25

The sum is $400 1/6$

To use the formula for the sum of a geometric sequence we first have to find out if the sum is finite. To check it we have to find $q$ :

$q=a_2/a_1=49/343=1/7$

Since $|q|<1$ we can say the sequence is convergent, so we can calculate the sum:

$S=a_1/(1-q)$

$S=343/(1-1/7)$

$S=343:6/7$

$S=343*7/6$

$S=2401/6$

$S=400 1/6$