Calculus
posted by Joshua .
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
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.
Respond to this Question
Similar Questions

Calculus
For what values of p>0 does the series Riemann Sum [n=1 to infinity] 1/ [n(ln n) (ln(ln n))^p] converge and for what values does it diverge? 
Calculus  ratio test
infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n>infinity)  [(e^n+1)/((n+1)!)] / [(e^n)/(n!)]  = lim (n>infinity)  [(e^n+1)/((n+1)!)] * [(n!)/(e^n)]  = lim (n>infinity)  ((e^n)(e^1)(n!)) … 
calculus  ratio test
Posted by COFFEE on Sunday, July 29, 2007 at 6:32pm. infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n>infinity)  [(e^n+1)/((n+1)!)] / [(e^n)/(n!)]  = lim (n>infinity)  [(e^n+1)/((n+1)!)] … 
calculus  ratio test
infinity of the summation n=1: (e^n)/(n!) [using the ratio test] my work so far: = lim (n>infinity)  [(e^n+1)/((n+1)!)] / [(e^n)/(n!)]  = lim (n>infinity)  [(e^n+1)/((n+1)!)] * [(n!)/(e^n)]  = lim (n>infinity)  ((e^n)(e^1)(n!)) … 
Calculus
What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx 
CALCULUS LIMITS
What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx 
CALCULUS
What is the following limit? lim as n goes to infinity of (pi/n) (sin(pi/n) + sin(2pi/n) + sin(3pi/n) +...+ sin(npi/n)) = I.) lim as n goes to infinity sigma (n and k=1) of pi/n sin(kpi/n) II.) Definite integral from 0 to pi of sin(x)dx 
Calc II
Use the comparison or limit comparison test to decide if the following series converge. Series from n=1 to infinity of (4sin n) / ((n^2)+1) and the series from n=1 to infinity of (4sin n) / ((2^n) +1). For each series which converges, … 
Algebra 1
Which of the following statements is true about the function ? 
Math
Which describes the end behavior of the graph of the function f(x)=2x^35x^2+x?