If CN = an / BN, TN is the sum of the first n terms of the sequence CN an=3n-1 bn=2*(1/3)^n

If CN = an / BN, TN is the sum of the first n terms of the sequence CN an=3n-1 bn=2*(1/3)^n

CN = BN / an, find the first n terms and TN of sequence CN
An = (2) nth power BN = 3n-1

an=2^n,bn=3n-1,cn=bn/an
So TN = 2 / 2 + 5 / 2 ^ 2 + 8 / 2 ^ 3 + 11 / 2 ^ 4 +... + (3n-1) / 2 ^ n
So 2tn = 2 + 5 / 2 + 8 / 2 ^ 2 + 11 / 2 ^ 3 +... + (3n-1) / 2 ^ (n-1)
So TN = 2tn TN = 2 + (5-2) / 2 + (8-5) / 2 ^ 2 + (11-8) / 2 ^ 3 +... + (3n-1-3n + 4) / 2 ^ (n-1) - (3n-1) / 2 ^ n
So TN = 2 + 3 * [1 / 2 + 1 / 4 + 1 / 8 +... + 1 / 2 ^ (n-1)] - (3n-1) / 2 ^ n
So TN = 2 + 3 * (1 / 2) * [1 - (1 / 2) ^ (n-1)] / (1 - 1 / 2) - (3n-1) / 2 ^ n
So TN = 2 + 3 * [1 - 2 ^ (1-N)] - (3n-1) * 2 (- n)
So TN = 2 + 3 - 6 * 2 ^ (- n) - (3n-1) * 2 ^ (- n)
So TN = 5 - (3N + 5) * 2 ^ (- n)
Inspection:
an=2,4,8,16,32,.
bn=2,5,8,11,14,.
cn=1,5/4,1,11/16,7/16,.
Tn=1,9/4,13/4,63/16,35/8,.
In TN general term formula:
T1=5 -(3*1+5)*2^(-1)=5 -8/2=1
T2=5 -(3*2+5)*2^(-2)=5 -11/4=9/4
T3=5 -(3*3+5)*2^(-3)=5 -7/4=13/4
T4=5 -(3*4+5)*2^(-4)=5 -17/16=63/16
T5=5 -(3*5+5)*2^(-5)=5 -5/8=35/8
. compliance

Note CN = an × BN to find the first n terms and TN of sequence {CN}
An = n-1 BN = (1 / 2) ^ (n-2) times

tn=(1-1)*(1/2)^(1-2)+(2-1)*(1/2)^(2-2)+.+(n-1)*(1/2)^(n-2)
tn/2=(1-1)*(1/2)^(2-2)+(2-1)*(1/2)^(2-2)+.+(n-1)*(1/2)^(n-1)
tn-tn/2=0*(1/2)^(-1)+(1/2)^0+(1/2)^1+.+(1/2)^(n-2)-(n-1)*(1/2)^(n-1)
tn/2=[1-(1/2)^(n-1)]/(1-1/2)-(n-1)*(1/2)^(n-1)
tn=4*[1-(1/2)^(n-1)]-2*(n-1)*(1/2)^(n-1)
tn=4-2*(1/2)^(n-2)-(n-1)*(1/2)^(n-2)
tn=4-(n+1)*(1/2)^(n-2)

If a is an odd number, then the two even numbers adjacent to a are______ ．

If a is an odd number, then the two even numbers adjacent to a are A-1 and a + 1, respectively

The difference between an even number and an odd number must be odd______ (judge right or wrong)

The analysis shows that the difference between an even number and an odd number must be odd

In natural numbers, the difference between the sum of the first 50 odd numbers and the sum of the first 50 even numbers is zero___________
You say 0 is not even or odd, 1st floor!

(1+3+5+...+99)-(0+2+4+...+98)
=(1-0) + (3-2) + (5-4) +... + (99-98) (50 pairs in total)
=50

After a sum minus one, is the difference odd, sum, odd or even?

A composite number - 1 = prime (e.g. 4 - 1 = 3)
A composite number-1 = composite number (e.g. 22-1 = 21)
A composite number - 1 = odd (e.g. 10 - 1 = 9)
A composite number - 1 = even (e.g. 9 - 1 = 8)
So a composite minus 1, the difference can be prime, composite, odd or even

In a positive integer, what is the difference between the sum of the first 20 even numbers minus the sum of the first 20 odd numbers?
A 20 B－20 C 40 D －40

Because positive integers don't include 0, so
First even minus first odd = 2-1 = 1
20*1=20
Choose a

It is known that the sum of squares of two consecutive odd numbers is equal to 130

Let them be x, x + 2
x^2+(x+2)^2=130
2x^2+4x-126=0
x^2+2x-63=0
(x-7)(x+9)=0
X = 7 or - 9
So these two consecutive odd numbers are 7 and 9 or - 9 and - 7

If the sum of squares of two adjacent even numbers equals 100, then the two even numbers are

If the sum of squares of two adjacent even numbers equals 100, then the two even numbers are 6 and 8