limits of sequences
a, Let q be the element of real numbers with q which is not equal to 0.
Show that if the absolute of q is less than 1, then
the limit of an absolute of q^n=0 as lim approaches positive infinity.
b, As the absolute of q which is greater than 1 then the
limit of an absolute of q^n =positive infinity as the limit approaches positive infinity.
c, What is the value of x if the sum of n=2 to positive infinity of (1+x)^-n=2
Use the ratio test,
Originally Posted by savetra
The infinite series,
But then the sequence must converge to zero,
Then multiplication by |q|>0 yields,
Again and again...
Thus the sequence is not bounded.