# Maple problem - matrices and sequences

1. May 29, 2010

### literacola

Maple problem -- matrices and sequences

Hello there Maple geniuses!

So I've been banging my head against these two problems for days and I was wondering if any of you had any idea how to proceed.

The first involves computing the limit of a series. The problem reads as follows:

"For large n, the sequence defined by

x1 = 2.30

xn = 9 * sqrt(xn-1+ 6)

approaches a limit. Find that limit correct to 15 significant figures, and then select the correct answer below."

The answer is supposedly 86.611..... but doesn't this approach infinity? I've attempted plotting the sequence out and computing many iterations of the sequence and as expected, the only thing the sequence does is blow up larger and larger. How can this possibly approach 86? What am I missing here?

My second problem deals with matrices and the problem is stated as follows:

For the matrix T given below, find T to the power of 1000 and then multiply it on the right by the column vector <1,0,0,0,0,0,0,0>.

T := < < 9/100, 19/100, 0, 1/50, 1/100, 0, 27/50, 3/20 > |

< 0, 0, 1/25, 13/100, 1/4, 1/10, 1/100, 47/100 > |

< 27/100, 1/10, 13/25, 0, 1/50, 1/100, 2/25, 0 > |

< 0, 9/50, 21/50, 0, 13/100, 1/10, 1/100, 4/25 > |

< 13/20, 0, 0, 0, 1/100, 3/100, 31/100, 0 > |

< 67/100, 23/100, 0, 1/50, 3/100, 0, 1/20, 0 > |

< 0, 0, 0, 33/100, 23/50, 3/100, 0, 9/50 > |

< 0, 7/10, 0, 0, 1/100, 1/25, 1/4, 0 > >;

So I assigned T to the matrix as shown above, and ran "PT := T^1000" to raise it to the 1000th power and assign it to the variable TP. Then to multiply against the column vector matrix V, I ran "TP.V". This gives me this huge list of numbers, and nothing that even resembles a matrix. The answer is supposedly the column vector <0.157,0.166,0.0872,0.141,0.0413,0.177,0.147> but I dont get anything near that.

Can anybody pleassssee help?