Show that the real sequence ( 0,-1,2,-3 , .... , (-1)nn, .... ) where n is a value from the set of Natural Numbers={0,1,2,..,n,..}, does not have an upper bound nor a lower bound.

Q: **) Define a sequence a1, a2, a3, ... as follows: a1 = 1, a2 = 3, and a, = an-1+ an-2 for al ategers…

A: The given sequence is 1,3,4,7,11,18,..... such that an=an-1+an-2 We have to prove P(n): an≤(74)n for…

Q: -) Determine the first six terms of the sequence defined by t₁ = -5 and t = 3t-1 + 8. 5, 23, -61,…

A:

Q: A sequence a,,a,,a,,a, a of real numbers is such that Can the arithmetic mean of {a,,a,,a,) be less…

A: The arithmetic mean of the sequence a1,a2,a3,⋯an is defined by the formula, A.M.=a1+a2+a3+⋯+ann…

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.