Sequences and series Definition and 58 Threads

Homework Statement Hi, it's been a while since I've done questions such as the one below. Does anyone know how to solve it? (Note that k and n are actually sub-k and sub-n). Thanks in advance. The kth term of a series, Sk = a (1-R^k) / (1-R) , is the sum of the first k terms of the...

I am not too sure what to do to answer this question. Each year for the past 5 years the population of a certain country has increased by a steady rate of 2.7% per annum. The present population is 15.2 million. a) what was thepopulation 1 yr ago? b) what was the population 5 years ago? I...

Hi I have a problem with sequences and series. Can anybody help, please? The question is For the sequence U1, U2, U3, ...Un... the terms are related by Un = Un-1 +2Un-2 where n is greater or equal to 1, U1=2 and U2 =5. Find the values of U7, U11, and U14. Can someone...

Does anyone know what are the uses of Sequences and Series in real life:confused:

I need to determine whether Sigma [sin(1/x)] for x=1 to x=infinity converges or diverges. I have a feeling that it diverges, but I don't know how to prove it. Thanks

I am teaching honors calculus in college, and trying to teach something about convergence of sequences and series. my class has apparently never seen a genuine proof in high school and have no idea how to begin one (answer: with the definition). I have had students ask me what "QED" stands...

Sequences and series... My textbook says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?

I'm trying to get an A in honors AlgII/Trig and it is impossible, but I won't give up, so I have a few questions. I'm not sure how to find the first two terms of a sequence (I got a few right, but most wrong and I don't know what's wrong). One of the problems is: a5 = 20; a8 = 4/25. I set...