Definition of exponential function: exponential function is a function in the form of "f(x)=a∧x", which requires a > 0 and a≠ 1.

When 0 < a < 1, the exponential function is a decreasing function; When a > 1, the exponential function is increasing function.

Exponential function always passes through fixed point (0, 1), range (0, +∞) and domain R.

Series:

Arithmetic progression: an=a 1+(n- 1)d, Sn=(a 1+an)n/2.

Geometric series: an=a 1*[q∧(n- 1)], Sn=(a 1-an)q/( 1-q) Note: This formula is in q ≠/kloc.

Or a 1=a2=...=an, sn = a1∧ n.

It is known that the formula of Sn for finding the general term of sequence an is: a1; When n≥2, an = sn-sn-1; Then substitute a 1 to see if n≥2 satisfies the general formula.

A n+ 1=p*an +q: Step 1, add q/(p-1) on both sides at the same time; Step 2, get that (an+q/(p- 1)) is a geometric series, then sum a 1 and the common ratio q/(p- 1) to get the general formula of an+q/(p- 1), and then subtract q from both sides at the same time.

Let's analyze some other problems in detail.