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High school mathematics (induction)
Sn+an=2n+ 1 ( 1)

s(n- 1)+a(n- 1)= 2(n- 1)+ 1(2)

( 1)-(2):a(n)+a(n)-a(n- 1)= 2。

2a(n) = a(n- 1) + 2

a(n)= 1/2 * a(n- 1)+ 1

Let a (n)+k =1/2 * (a (n-1)+k), and k = -2 is obtained.

a(n)-2 = 1/2 *(a(n- 1)-2)

And s1+a1= 2a1= 2 * n+1= 3.

a 1 = 3/2,

a(n)-2 =( 1/2)^(n- 1)*(3/2-2)=( 1/2)^n

a(n)= 2+( 1/2)^n(n & gt; =2)

a2 = 2 + ( 1/2)^2 = 9/4

a3 = 2 +( 1/2)^3 = 17/8