SOLUTION: Calculate the difference between Sinfinity to S7of 4+4/3+4/9+....

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Question 848493: Calculate the difference between Sinfinity to S7of 4+4/3+4/9+....
Answer by swincher4391(1107) About Me  (Show Source):
You can put this solution on YOUR website!
Geometric series with a = first term and r = common ratio and n = # of terms
Finite Geometric series a%2A%28%281-r%5En%29%2F%281-r%29%29
Infinite Geometric series a%2F%281-r%29
S_7 n = 7, a = 4, r = 1/3 4%2A%28%281-%281%2F3%29%5E7%29%2F%281-%281%2F3%29%29%29+=+4372%2F729+

S_inf a=4, r=1/3 4%2F%281-%281%2F3%29%29 = 6
6-+%284372%2F729%29+=++highlight%282%2F729%29
Alternative method:
Calculating a%2F%281-r%29++-+a%2A%28%281-r%5En%29%2F%281-r%29%29
a%2F%281-r%29++-+%28a-ar%5En%29%2F%281-r%29%29
ar%5En%2F%281-r%29

%284%2A%281%2F3%29%5E7%29%2F%281-%281%2F3%29%29++=+highlight%282%2F729%29