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evaluate the infinite geometric series,

 

7 to the power of 0 over 100 to the power of 1 + 7 to the power of 1 over 100 to the power of 2 + 7 to the power of 2 over 100 to the power of 3 + ...

 

as a fraction and find the first 6 digits in its decimal expansion.

 Dec 19, 2022
 #2
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[7^0 / 100^1]  +  [7^1 / 100^2]  +  [7^2 / 100^3]  + ..........and so on. Is it right?

 

(1 / 100, 7 / 10000, 49 / 1000000, 343 / 100000000, 2401 / 10000000000, 16807 / 1000000000000, 117649 / 100000000000000, 823543 / 10000000000000000, 5764801 / 1000000000000000000, 0.0000000000 0040353607, 0.0000000000 0002824752 49.......and so on

 

sumfor(n, 0, 10000, (7^n / (100^(n+1))))==0.01075268817 - sum of infinite G. S.

 

OR:

 

Sum ==F / [1  -  R], where F==First term,  R==Common Ratio

Common Ratio ==7 / 100

 

Sum ==[1 / 100] / [1  -  7/100]==1/100  x  100/93==100 / 9,300 ==0.01075268817 - sum of infinite G. S.

 Dec 20, 2022

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