✔ 最佳答案
1. find the sum of the integers from 501 to 1000 inclusive
SUM
=n/2[2a+(n-1)d]
=500/2[2*501+(500-1)]
=250(1501)
=375250
2.find the sum of the arithmetic series
2+5+8+.....+398
let 2+3(n-1)=398
3(n-1)=396
n-1=132
n=133
SUM
=n/2[2a+(n-1)d]
=133/2[2*2+3(133-1)]
=26600
3.two sequences U1,U2,U3,....are defined as follows
Sequence A: U1=2, Un+1=3-Un1
Sequence B: U1=2, Un+1=Un+1/2^n
(a)
Sequence A
U1=2
U2=3-U1=3-2=1
U3=3-U2=3-1=2
U4=3-U3=3-2=1
U5=3-U4=3-1=2
Sequence B
U1=2
U2=U1+1/2=5/2
U3=U2+1/2^2=11/4
U4=U3+1/2^3=23/8
U5=U4+1/2^4=47/16
(b)
Sequence A is oscillating
Sequence B is convergence because
Un+1-Un=1/2^n
when n tends to infinity, the difference between two terms will tend to 0
So it is convergence.