#18 prove induction 10^n 3^n is divisible factor divides 7 for all positive integer mathgotserved

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Prove
1) 1+2+3+...+n=n(n+1)/2 ----------------------------- https://tinyurl.com/tou5rob
2) 2+2^2+2^3+...+2^n=2(2^n-1) -------------------- https://tinyurl.com/rmnoubd
3) 1+5+9+...+(4n-3)=n(2n-1)---------------------------https://tinyurl.com/tp9csgv
4) 1/(1X2)+1/(2X3)+...+1/(n(n+1))=n/(n+1), https://tinyurl.com/rp6wg57
5) n^3+2n is divisible by 3,----------------------------https://tinyurl.com/rkjtrsx
6) n less 2n----------------------------------------------------https://tinyurl.com/wp9tqfe
7) 1+3+5+7+...+(2n-1)=n^2 for all n in N,-----https://tinyurl.com/safzdmc
8) sum Σ k=1 to n k^2= 1/6n(n+1)(2n+1)----https://tinyurl.com/v3jcw3z
9) 9^n-2^n id divisible by 7,----------------------------https://tinyurl.com/v3jcw3z
10) 1+5+9+13+..+(4n-3)=½n(4n-2)----------------https://tinyurl.com/v3jcw3z
11) n Σ k =n(n+1)/2 sum of k n plus one over two---https://tinyurl.com/wratyjw
12) 1^3+2^3+3^3+..+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4,-----https://tinyurl.com/qrcgnb3
13) 10^1+10^2+10^3+...+10^n=10/9(10^n-1),----------------https://tinyurl.com/v96s345
14) d/dx (x^-1)=(-1)^nn!/x^(n-1)-----------------------https://tinyurl.com/sb8sfbh
15) 2^n greater or equal 1+n,------------------------ https://tinyurl.com/tbth2cz
16) 3^n less than (n+1)!,--------------------------------https://tinyurl.com/tvd6pqk
17) 8^n-1 is divisible by 7,-----------------------------https://tinyurl.com/udnvmwv
18) 10^n-3^n is divisible by 7-------------------------https://tinyurl.com/wncts9h
19) 5^n-2^n is divisible by 3--------------------------https://tinyurl.com/vafdffj

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