Find sequence 1 / 2, 3 / 4, 5 / 8, 16 / 17 The sum of the first n terms of 2N-1 / 2 ^ n Sn = 1×1/2 + 3×1/4 + 5×1/8 + ...+ (2n-3)/2^(n-1) + (2n-1)/2^n Sn/2 = 1×1/4 + 3×1/8 + 5×1/16 + ...+ (2n-3)/2^n + 2n-1/2^(n+1) Sn - Sn/2 = 1/2 - 1 + 2( 1/2 + 1/4 + 1/8 + ...+ 1/2^n ) - 2n-1/2^(n+1) Sn = -1/2 + 2×(1/2)×(1-1/2^n)/(1-1/2) - 2n-1/2^(n+1) = 3 - (2n+3)/2^n Why is the third step Sn - Sn / 2 = 1 / 2 - 1... Where does this - 1 come from?

Find sequence 1 / 2, 3 / 4, 5 / 8, 16 / 17 The sum of the first n terms of 2N-1 / 2 ^ n Sn = 1×1/2 + 3×1/4 + 5×1/8 + ...+ (2n-3)/2^(n-1) + (2n-1)/2^n Sn/2 = 1×1/4 + 3×1/8 + 5×1/16 + ...+ (2n-3)/2^n + 2n-1/2^(n+1) Sn - Sn/2 = 1/2 - 1 + 2( 1/2 + 1/4 + 1/8 + ...+ 1/2^n ) - 2n-1/2^(n+1) Sn = -1/2 + 2×(1/2)×(1-1/2^n)/(1-1/2) - 2n-1/2^(n+1) = 3 - (2n+3)/2^n Why is the third step Sn - Sn / 2 = 1 / 2 - 1... Where does this - 1 come from?

Because 1 / 2 of 2 (1 / 2 + 1 / 4 + 1 / 8 +... + 1 / 2 ^ n) is made up,
In order to keep the value of the original formula unchanged, 1 should be subtracted

Try to find 5 / 2,17 / 4,49 / 8129 / 16 The sum of the first n terms of, 2n + 1 / 2 ^ n

Sum 2n and 1 / 2 ^ n separately
Sn1=(2+2n)n/2=(n+1)n
Sn2=1/2×(1-(1/2)^n)/(1-1/2)=1-1/2^n
Sn=Sn1+Sn2=n^2+n+1-1/2^n

General term formula of sequence-1, - 7 points 15,9 points 24
series
-1
-15 out of 7
24 out of 9 and so on
Find the general term formula of the sequence

An=[(-1)^n](2n+1)/n(n+2)

Multiple choice questions on the definition of sequence limit
The convergence of sequence {xn} to real number a is equivalent to ()
For any given E > 0, a has an infinite number of sequences in (A-E, a + e)
For any given E > 0, B has finite multinomial with sequence in (A-E, a + e)
For any given E > 0, C has an infinite number of sequences outside (A-E, a + e)
For any given E > 0, D has finite multinomial with sequence outside (A-E, a + e)
Why can't I understand outside (A-E, a + e),

The answer D is obvious, I think you should have a little doubt about a ~ A is really confused, but it's wrong to think about it carefully. The main reason is that infinity is not all items, such as sequence 1,0,1,0,1,0. Such a sequence has infinity near 0, that is, 0 itself, but obviously the sequence itself does not converge. If you have questions about D, I suggest you read a book, ha ha,