1+(1/2)+(1/4)+(1/8)-(1/16)-(1/32)-(1/64)… up to infinity
I can't come up with the pattern this series is following. I know that it's similar to (1/(2^n)) but I dont know with it alternates after every four. Thank you in advance!
I can't come up with the pattern this series is following. I know that it's similar to (1/(2^n)) but I dont know with it alternates after every four. Thank you in advance!
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1+(1/2)+(1/4)+(1/8)-(1/16)-(1/32)-(1/64)… up to infinity
= [ 1+(1/2)+(1/4)+(1/8) ] * [ 1 - 1/16 + 1/256 - ...]
= 15/8 * (1/(1+1/16)) the latter term being the sum of a GP with common ratio -1/16
=15/8 * 16/17
=30/17
= [ 1+(1/2)+(1/4)+(1/8) ] * [ 1 - 1/16 + 1/256 - ...]
= 15/8 * (1/(1+1/16)) the latter term being the sum of a GP with common ratio -1/16
=15/8 * 16/17
=30/17
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it alternates every 4?
1 + 1/2+ 1/4 + 1/8 = 15/8
-1/16 - 1/32 - 1/64 - 1/128 = 15/8(-1/16)
15/8 * (1 - 1/16 + (1/16)^2 - (1/16)^3....)
15/8 (1/(1+1/16))
15/8*(16/17)
30/17
1 + 1/2+ 1/4 + 1/8 = 15/8
-1/16 - 1/32 - 1/64 - 1/128 = 15/8(-1/16)
15/8 * (1 - 1/16 + (1/16)^2 - (1/16)^3....)
15/8 (1/(1+1/16))
15/8*(16/17)
30/17