Sequence 2 / 3, - 3 / 9,4 / 27, - 5 / 81 A general formula of is

Sequence 2 / 3, - 3 / 9,4 / 27, - 5 / 81 A general formula of is

1,3,9,27,81... What is the sequence? Ten square sequence? Find out the law, do not know what is the sequence,

A1=3^0
A2=3^1
A3=3^2
.
This is an equal ratio sequence
The common ratio is 3. You should be careful
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The sum of the first n terms of the sequence {n-1 power of 1 + 2} is? Please explain in detail. Thank you

You can understand it as the sum of two sequences, that is, the sum of the N-1 power of 1 and 2
The sum of the first n terms is 1 + 1 + 1 + n terms = 1xn = n
The sum of the first n terms of the N-1 power of 2 is the n-th power of (1-2) / (1-2) = 2
So the sum of the first n terms is the nth power of N + 2
In short, the topic is divided into the sum of two sequences, one is a constant sequence, the other is an equal ratio sequence

The first n terms and Sn of sequence 1,1 + 2 / 1,1 + 2 + 3 / 1 are

According to the meaning of the question, an = 1 / (1 + 2 +... + n) where 1 + 2 + 3 +... + n = n (n + 1) / 2, so an = 2 / N (n + 1) notice the characteristic of 1 / N (n + 1) = 1 / N - 1 / (n + 1), we do the transformation: the first n terms of an = 2 / N - 2 / (n + 1) sequence and: SN = a1 + A2 + a3 +. + an = 2 / 1-2 / 2 + 2 / 2-2 / 3 + 2 / 3-2 / 4 +... +

Find sequence 0,1,1,2,2,3,3,4,4 The first n terms and Sn of

Just sum the even and odd terms separately
When n is odd:
Sn=2*(1+2+…… （n-1）/2)=(n^2-1)/4
When n = K + 1 is even
Sn=Sk+an=(k^2-1)/4+n/2=n^2/4

Sequence 3, 33333 The first n terms and Sn of=

Sequence 3, 33333 The general term formula of
an=1/3*(10^n-1)=1/3*10^n-1/3
=10/3*10^(n-1)-1/3
Sn=10/3*(1-10^n)/(1-10)-n/3
=10/27(10^n-1)-n/3

Sequence 1,1 + 2,1 + 2 + 3, + ＋n,… The first n terms and Sn of

n*(n+1)*(n+2)/6
Specific process support questioning

In the sequence {an}, the first n terms and Sn = 3 ∧ n + 1
(1) find A1
(2) find the general term formula an
(3) is the sequence an equal ratio sequence

1. A1 = S1 = 3 to the power of 1 + 1 = 42. This kind of problem can be solved by "write it again" Sn = 3 to the power of N + 1s (n + 1) = 3 to the power of (n + 1) + 1s (n + 1) - Sn = an, then 3 to the power of (n + 1) + 1 - (3 to the power of N + 1) = an = 3 to the power of (n + 1) - 3 to the power of N, and then extract the common factor, 3 to the power of (n + 1) = 3 to the power of n

If the sequence: 1,2,4,7,11 ① What's the tenth number? 2. What's the nth number?
If the sequence: 1,2,4,7,11
① What's the tenth number? 2. What's the nth number?

an=a(n-1)+(n-1)
=a(n-2)+(n-1)+(n-2)
=a1+(n-1)+(n-2)+...+1
=1+n(n-1)/2 (n=1、2、3、4、……）
So the tenth number = 1 + 10 × (10-1) / 2 = 1 + 45 = 46
The nth number is 1 + n (n-1) / 2 (n = 1, 2, 3, 4,...)

What is the number after 1 / 2 3 / 2 5 / 6 11 / 30

The denominator of the latter is the product of the numerator of the former, and the numerator is the sum of the numerator of the former
Therefore, the denominator of the latter number is 11 * 30 = 330, and the numerator is 11 + 30 = 41
The last number is 41 / 330