1.0 < x < π/2 means 0; 1, and x ((sinx) 2) < 1 is equivalent to xsinx < 1/sinx,

Second, according to the definition, let am=a 1+(m-a)d, then an=a 1+(n-a)d, and two expressions are subtracted to get d=(b-a)/(n-m).

According to the definition, let BM = a (q (m- 1)), then BN = a (q (n- 1)), and divide the two formulas to derive Q = (b/a) (n-m).

3. Let an=n+ 1, then the black circle code is sn, so Sn = (2+n+1) n/2 = (n+1.5) 2-2.25.

Get n= parentheses (root number (4022.5)- 1.5) (I don't know how to spell parentheses, which means rounding). The root number of 4022.5 is about 63.42, so 63.42- 1.5=6 1.92.

So n satisfying the proposal is 6 1.

Fourthly, according to the definitions of am=a 1+(m-a)d and Sn=Sm, a 1+(m-n)d/2=0 is deduced, and another formula of Sn+m is obtained.

I don't understand the second one. Geometric series don't know what the definition of positive term is. If an = q (n-b) (b is an integer), then Tn should be the product of the first n terms, so the above conclusion can be used in this problem.