#22 Proof Principle of Mathematical induction mathgotserved 1^2+2^2 +3^2++ n^2 nn+12n+1 6

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Prove
1) 1+2+3+...+n=n(n+1)/2 ----------------------------- tinyurl.com/to...
2) 2+2^2+2^3+...+2^n=2(2^n-1) -------------------- tinyurl.com/rm...
3) 1+5+9+...+(4n-3)=n(2n-1)---------------------------tinyurl.com/tp...
4) 1/(1X2)+1/(2X3)+...+1/(n(n+1))=n/(n+1), tinyurl.com/rp...
5) n^3+2n is divisible by 3,----------------------------tinyurl.com/rk...
6) n less 2n----------------------------------------------------tinyurl.com/wp...
7) 1+3+5+7+...+(2n-1)=n^2 for all n in N,-----tinyurl.com/sa...
8) sum Σ k=1 to n k^2= 1/6n(n+1)(2n+1)----tinyurl.com/v3...
9) 9^n-2^n id divisible by 7,----------------------------tinyurl.com/v3...
10) 1+5+9+13+..+(4n-3)=½n(4n-2)----------------tinyurl.com/v3...
11) n Σ k =n(n+1)/2 sum of k n plus one over two---tinyurl.com/wr...
12) 1^3+2^3+3^3+..+n^3= (n(n+1)/2)^2 n^2(n+1)^2/4,-----tinyurl.com/qr...
13) 10^1+10^2+10^3+...+10^n=10/9(10^n-1),----------------tinyurl.com/v9...
14) d/dx (x^-1)=(-1)^nn!/x^(n-1)-----------------------tinyurl.com/sb...
15) 2^n greater or equal 1+n,------------------------ tinyurl.com/tb...
16) 3^n less than (n+1)!,--------------------------------tinyurl.com/tv...
17) 8^n-1 is divisible by 7,-----------------------------tinyurl.com/ud...
18) 10^n-3^n is divisible by 7-------------------------tinyurl.com/wn...
19) 5^n-2^n is divisible by 3--------------------------tinyurl.com/va...
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