set 4 - sequences and series harder solutions - Sequences and series Sequences For the following sequences determine whether they converge or diverge If

# set 4 - sequences and series harder solutions - Sequences...

• Essay
• 15

This preview shows page 1 - 5 out of 15 pages.

Sequences and seriesSequencesFor the following sequences determine whether they converge or diverge.If possible alsodetermine the limits for those among the sequences that converge.1.n-1n2-1Answer.Rewrite as1-1nn-1n.Asngoes to infinity the numerator goes to 1 and the denominator to +. We concludethat the limit of this sequence is 0. Formally this can be written aslimn→∞n-1n2-1= limn→∞1-1nn-1n=1-limn→∞1nlimn→∞(n-1n)=1limn→∞n= 0.2.2--12n 3.sin1n
5.2 + cos(n)n 7.fn+1fn,wherefndenotes thenth Fibonacci number.
8. Turn the following infinite expression into a sequence.s2 +r2 +q2 +2 +...If this sequence converges, what is its limit? 9. Turn the following infinite expression into two different sequences...+s2 +r2 +q2 +2If these sequences converge, what are their limits?