?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#