Posted by Joshua on Thursday, April 16, 2009 at 10:47pm.
Does the series (1+sin(n))/(10^n) from summation 0 to positive infinity converge or diverge?
I let an = (1+sin(n))/(10^n) and bn = 1/10^n
lim as n approaches positive infinity = an/bn = ((1+sin(n))/(10^n))/(1/(10^n))= 1+sin(n)= positive infinity.
I don't know if it's right or not but if someone could look over it that would be great.

Calculus  Reiny, Friday, April 17, 2009 at 8:37am
I ran this simple QuickBasic program
FOR N = 1 TO 20
TERM = (1+ SIN(N))/(10^N)
SUM = SUM + TERM
PRINT TERM, SUM
NEXT N
the terms keep getting smaller by appr a factor of 10, (obviously the denominators become 1,10,100,1000, ...)
since the sin(N) can only be a number between 1 and 1, then (1+sin(n)) will range between 0 and 2
after about 7 terms, the sum had approached a value of 1.204407 and since each successive term would be smaller than 10^7, it would converge to that sum.
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