Step (1)
We know that the sum of all the terms in an infinite geometric sequence finding from following equation whenever |q| < 1 .
q = magnitude
So :
Remember it I'll use it again.
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Step (2)
We know that the sum of the n first terms of a geometric sequence finding from following equation.
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Sum of all terms starting from the third is 9.
So :
Sides minus 9
So :
Factoring t(1)
We have found t(1) = 81 ( 1 - q ) in step (1).
So :
Divided sides by 81
Subtract sides minus -1
Negatives simplifies
Radical sides
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Step (4)
If q = 1/3 :
So :
°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°°
If q = - 1/3 :
So :
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And we're done.
Thanks for watching buddy good luck.
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