The sum of the first n items of high school mathematics sequence The leading formula is 2n + 1-3 ^ n / 2 ^ n. help to find the sum of the first n terms of the leading formula. Thanks. (n > 1)

The sum of the first n items of high school mathematics sequence The leading formula is 2n + 1-3 ^ n / 2 ^ n. help to find the sum of the first n terms of the leading formula. Thanks. (n > 1)

The solution is divided into two parts
S=2n＋1－3^n／2^n
A=2n＋1 ; B=3^n／2^n
There are: sequence a is equal difference sequence, sequence B is equal ratio sequence
An=n(n+1)+n ; Bn=3(3/2)^n-3
Sn=An-Bn
=n^2+2n+3-3(3/2)^n

For an arithmetic sequence with 2n + 1 terms, the ratio of the sum of odd terms to the sum of even terms is----

Let the first term of the original sequence be a and the tolerance be d,
The original sequence is a, a + D, a + 2D, a + 3D,. A + 2nd
The odd number terms are: A, a + 2D, a + 4D,. A + 2nd
Sum of odd terms: s odd = [a + (a + 2nd)] (n + 1) / 2 = (a + nd) (n + 1)
The even number terms are: a + D, a + 3D, a + 5D,. A + (2n-1) d
Even sum = [(a) + (d) + (a) + (d)
S odd / s even = (n + 1) / n
explain:
This problem only needs to use the summation formula of arithmetic sequence: (first term + last term) × number of terms △ 2

If the number of terms n of the arithmetic sequence {an} is odd, the ratio of the sum of odd terms to the sum of even terms is ()
A. n−1nB. 2n+1nC. n+1n−1D. 2n+12n

The sum of odd items is n + 12 & nbsp; a1 + N + 12 · n − 122 · 2D = n + 12 & nbsp; (a1 + n − 12D & nbsp;), and the sum of even items is n − 12 (a1 + D) + n − 12 · n − 322 · 2D = n − 12 & nbsp; (a1 + n − 12D & nbsp;)

If an arithmetic sequence has 2n + 1 terms, the ratio of the sum of odd terms to the sum of even terms is

One of the summation formulas of arithmetic sequence:
(first item + last item) * number of items / 2
You can divide this arithmetic sequence into an arithmetic sequence composed of odd items (n + 1 items) and an arithmetic sequence composed of even items (n items). The first and last items of these two subsequences are equal, so the corresponding sum ratio is n + 1: n

The odd number has (). The even number has ()

The odd numbers are (9,15) and the even numbers are (4,6,8,10,12,14,16,18)

Odd numbers within 20 even numbers within 20 all even numbers 50 within 4
Odd numbers within 20 even numbers within 20 all even numbers within 50 all multiples within 4 even numbers within 50 all multiples within 6

Odd number 1 3 5 7 9 11 13 15 17 19
Even numbers 0,2,4,6,8,10,12,14,16,18,20