1. Home
  2. Calculus
  3. Sequence and series

Introduction to sequences - Sequence and series

Introduction to sequences


1. If a sequence has the limit LL, then we can say that:

lim\limn →\infty aann=L=L

If the limit is finite, then it is convergent. Otherwise, it is divergent.

2. If the limit of the sequences {ana_n} and {bnb_n} are finite and cc is constant, then we can say that

i) lim\limn →\infty (an+bn)=lim(a_n+b_n)=\limn →\infty an+a_n+lim\limn →\infty bnb_n.
ii) lim\limn →\infty (anbn)=lim(a_n-b_n)=\limn →\infty ana_n-lim\limn →\infty bnb_n.
iii) lim\limn →\infty can=cca_n=c lim\limn →\infty ana_n.
iv) lim\limn →\infty(anbn)=(a_nb_n)= lim\limn →\inftyana_n* lim\limn →\infty bnb_n.
v) lim\limn →\infty [an[a_n÷\divbn]b_n] =lim=\limn →\inftyana_n÷\div lim\limn →\inftybnb_n,, bn0b_n\neq0.

3. If ancnbna_n\leq c_n\leq b_n and lim\limn →\infty an=a_n= lim\limn →\infty bn=Lb_n=L, then lim\limn →\infty cn=Lc_n=L.

4.if lim\limn →\infty an=0|a_n|=0, then lim\limn →\infty an=0a_n=0 as well.

5. We say that:

Where the sequence {xnx^n} is convergent for -1< xx \leq 1, and divergent if xx > 1.
  • 1.
  • 2.
    Finding the terms of a sequence

    Find the first five terms of the following sequences.
  • 3.
    Finding the formula for a sequence

    Find the formula for the general term ana_n for the following sequences
  • 4.
    Convergence and divergence of sequences

    Evaluate the limits and determine if the following limits are converging or diverging.
Teacher pug

Introduction to sequences

Don't just watch, practice makes perfect.

We have over 1090 practice questions in Calculus for you to master.