SOLUTION: find the sum of the inifinite seires if it is not possible write no sum and explain why 1. 1024+512+256+128+... 2. 1/9+1/3+1+3... 3. 16+4+1+1/4... i do not understand how to

Algebra ->  Trigonometry-basics -> SOLUTION: find the sum of the inifinite seires if it is not possible write no sum and explain why 1. 1024+512+256+128+... 2. 1/9+1/3+1+3... 3. 16+4+1+1/4... i do not understand how to      Log On


   

Question 763709: find the sum of the inifinite seires if it is not possible write no sum and explain why
1. 1024+512+256+128+...
2. 1/9+1/3+1+3...
3. 16+4+1+1/4...
i do not understand how to solve this.
Answer by Tatiana_Stebko(1539) About Me  (Show Source):
You can put this solution on YOUR website!
Sum of an Infinite Geometric Series when abs%28r%29%3C1 is
S=a%5B1%5D%2F%281-r%29
1) 1024%2B512%2B256%2B128+...
a%5B1%5D=1024,a%5B2%5D=512, r=a%5B2%5D%2Fa%5B1%5D=512%2F1024=1%2F2, since abs%28r%29%3C1
S=1024%2F%281-1%2F2%29=2048
Answer: 2048
2) 1%2F9%2B1%2F3%2B1%2B3+...
a%5B1%5D=1%2F9,a%5B2%5D=1%2F3, r=a%5B2%5D%2Fa%5B1%5D=%281%2F3%29%2F%281%2F9%29=3, since r%3E1
it is not possible to find the sum
Answer: No sum
3)16%2B4%2B1%2B1%2F4+...
a%5B1%5D=16,a%5B2%5D=4, r=a%5B2%5D%2Fa%5B1%5D=4%2F16=1%2F4, since abs%28r%29%3C1
S=16%2F%281-1%2F4%29=64%2F3
Answer: 64%2F3