Calculus
posted by Raaki .
If a_n>0 and a_(n+1) <= a_n, does the alternating series ∑ ((1)^(n+1)) a_n converge or diverge?

a quick web search will reveal that the alternating series converges.
Respond to this Question
Similar Questions

math
Write the arithmetic sequence 21,13,5,3... in the standard form: a_n= a_n=a_1+(n1)dso a_n=21+(n1)8 *a_n=1688n why isnt this right? 
calculus
A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? 
Discrete Math
Solve the recurrence relation a_n = 2a_n1 + 15a_n2, n ≥ 2, given a₀ = 1, a₁ = 1. x² + 2x  15, the distinct roots 3 and 5, so a_n = C₁(3^n) + C₂(5)^n. The initial condition gives a₀ = 1 = … 
Calculus
Find a series ∑a_n for which ∑(a_n)^2 converges but ∑a_n diverges 
Calculus
If a_n >0 and b_n >0 and series ∑ sqrt( (a_n)^2 +(b_n)^2 ) converges, then ∑a_n and ∑b_n both converge. True or false? 
Calculus
If a_n does not equal zero for any n>=1 and ∑a_n converges absolutely, then ∑ 1/a_n diverges. The series are from n=1 to infinity. I think this is true but I'm not sure. 
Algebra
find the arithmetic mean A_n1_3.9, A_n+1_=7.1 
mathematical statistics
Suppose a_n∈ [0,1] and X_n is a sequence of i.i.d random variables with p.d.f : p(X_n=1)= p(X_n= 1)=0.5 . ∑_(n=1)^∞▒a_n X_n is convergent with probability 1, is ∑_(n=1)^∞▒a_n^2 convergent? 
Algebra
For the following sequences determine the term indicated: a_1=2, a_n=2(a_n1)^2,a_4 a_n=ln(e^n+2), a_5 b_0=1, b_1=2, b_n+1=2b_nb_0 
DISCRETE MATH
Determine whether the following is a recursive or explicit. Then, find the first four terms of the following sequence. a) a_n = 〖na〗_(n1) where a_0 =5 b) a_n = a_(n1) + 3a_(n2) where a_0 = 1 and a_1 =2 c) a_n = 2^n …