数列前n项和

1+2+3+4+5+6+7+8+9+…+n=n(n+1)/2 

1+3+5+7+9+11+13+15+…+(2n-1)=n2 
  2+4+6+8+10+12+14+…+(2n)=n(n+1) 1^2+2^2+3^2+4^2+5^2+6^2+7^2+8^2+…+n^2=n(n+1)(2n+1)/6 
  

1^3+2^3+3^3+4^3+5^3+6^3+…n^3=(n(n+1)/2)^2 1*2+2*3+3*4+4*5+5*6+6*7+…+n(n+1)=n(n+1)(n+2)/3

等差数列:an=a1+(n-1)d 
     Sn=[(a1+an)*n]/2 
       =a1*n+n*(n-1)d/2 


等比数列:an=a1*q^(n-1) 
    Sn=[a1（1-q^n)]/(1-q)
      =(a1-an*q)/(1-q) 

1.a^(log(a)(b))=b 

2.log(a)(MN)=log(a)(M)+log(a)(N); 

3.log(a)(M/N)=log(a)(M)-log(a)(N); 

4.log(a)(M^n)=nlog(a)(M) 



性质一：换底公式 

log(a)(N)=log(b)(N) / log(b)(a) 

性质二：

log(a^n)(b^m)=m/n*[log(a)(b)] 

公式三:

log(a)(b)=1/log(b)(a)