**TI86** Program file dated 06/23/04, 19:57 ø čZTHEOR1AčæāTo7ZINITo4ZLoŽD0/D25/-SEQUENCES AND SERIESo-n 4ltn-p=1 4lboD0 2xnD43 2yn6ZSUMnŽD11/D14/-1=noD45 2xnD38 2yn6ZSUMnŽD16/D58/-p=(n(n+1))/2oD15 2xnD21 2yn6ZSUMnŽD33/D28/-p=(n(n+1)(2n+1))/6o4ZKoLD1/4MO/4T1/D2/4PR/3X/D4/4EX/3X/D5/4QU/3QoāT1oƒo4ZLoD0 2xnD45 2yo6ZSUMoŽD9/D13/-p^3=(n(n+1))/4oD15 2xnD22 2yo6ZSUMoŽD32/D28/-p(p+1)=(n(n+1)(n+2))/3o4ZKoLD1/4MO/4T2/D2/4PR/3T/D4/4EX/3X/D5/4QU/3QoāT2oƒo4ZLoD0 2xnD45 2yo6ZSUMoŽD9/D12/-p(p+1)(p+2)=n(n+1)(n+2)(n+3)/4o-k 4ltn-i=1 4lboD14 2xnD25 2yo6ZSUMoŽD29/D26/-xA(i)=xoD50 2xnD25 2yo6ZSUMoŽD29/D62/-A(i)o4ZKoLD1/4MO/4T3/D2/4PR/4T1/D4/4EX/3X/D5/4QU/3QoāT3oƒo4ZLoD0 2xnD45 2yo6ZSUMoŽD9/D12/-r^(i-1)=(1-r^k)/(1-r)oŽD26/D0/-THE STUDY OF ANTIDERIVITIVES WILLoŽD33/D0/-ILLUMINATE THE PROCESS OF CONVERT-oŽD40/D0/-ING SUMMATION TO ALGEBRA.o4ZKoLD1/4MO/4T4/D2/4PR/4T2/D4/4EX/3X/D5/4QU/3QoāT4oƒo4ZLoŽD0/D0/-FINITE GEOMETRIC SERIESoŽD6/D0/-Sn=A+Ax+Ax+...Ax^(n-2)+Ax^(n-1)oŽD21/D0/-Sn=oD14 2xnD33 2yo-n=0 4lbn-n-1 4lto6ZSUMoŽD21/D28/-Ax^n=A(1-x^n)/(1-x),{x1}oŽD28/D28/-AN INFINITE GEO. SERIESoŽD35/D28/-LOOKS LIKE THE ABOVE WITHoŽD41/D0/-+..., MEANING WITHOUT END.o4ZKoLD1/4MO/4T5/D2/4PR/4T3/D4/4EX/3X/D5/4QU/3QoāT5oƒo4ZLoŽD0/D0/-AS n NEARS INFINITY(~), IF |x|<1,oŽD6/D0/-THEN IT CONVERGES TO Sn=A/(1-x).oŽD12/D0/-IF |x|>1, THEN THE SERIES DOESoŽD18/D0/-NOT CONVERGE TO A FINITE SUMoŽD24/D0/-HENCE WE HAVE NO WAY OF KNOWINGoŽD30/D0/-THE VALUE OF Sn. ie.1+.5+.25+.125+...oŽD36/D0/-=1+.5+.5+.5^3+...: S=1/(1-.5)=2o4ZKoLD2/4PR/4T4/D4/4EX/3X/D5/4QU/3QoāQnD1 3KoāXoß'Ē