Infinite Sum
Hi, I'm having trouble solving this problem:
Sum of( 2(1/4)^k + 3(-1/5)^k) from k=0 to infinity
I get a sequence of partial sums of:
Sn= 2 + 3 + 2/4 - 3/5 + 2/4^2 + 3/5^2 + 2/4^3 - 3/5^3 + ... + 2/4^n +
3*(-1/5)^n
And looking at it I'm pretty sure that it's a collapsing series. But I
don't see what cancels out.
.
Relevant Pages
- Re: abundance of irrationals!)
... BUT THAT'S JUST A DIVERSION AWAY FROM YOUR FAILURE TO STATE YOUR CLAIMED ALTERNATIVE DEFINITION OF SUM1/2^k AS DISTINCT FROM A LIMIT OF A SEQUENCE OF PARTIAL SUMS. ... >> as a binary representation of unity, ... is not defined by the standard limit of a sequence of partial sums, YOU must state YOUR definition of 0.111... ...
(sci.math) - Re: .99999... still=/= 1
... This is COMPLETE NONSENSE. ... sequence itself is not equal to 1 (and this question doesn't even ... This is nonsense --- partial sums don't have anything to do with it. ... of a decimal expansion of pi is NOT the number pi. ...
(sci.math) - Re: abundance of irrationals!)
... leads to the infinite string 0.111..., ... (of the partial sums) ... is not part of the bijection of the sequence with N. ... as a binary representation of unity, your "explanation" amounts to another refusal to say what is your non-standard definition. ...
(sci.math) - Re: Attempts to Refute Cantors Uncountability Proof?
... glue the whole s-size pieces onto the assembly to the left, ... This is the sort of intuitive understanding of the meaning of .333... ... infinite series as the limit of the sequence of partial sums. ...
(sci.math) - Re: Attempts to Refute Cantors Uncountability Proof?
... infinite series as the limit of the sequence of partial sums. ... service to the orthodox canon, accept it as truth, or transfer to ...
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