I tried to do these questions, however I can't seem to get the answer. Can someone help me? I would really appreciate it.
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Mathematical Induction
Prove that the statement in true for every positive integer n.
1. 1/1*2*3 + 1/2*3*4 + 1/3*4*5 + .... + 1/n*(n+1)*(n+2)
2. 1+2*2+3*2^2+...+n*2^n-1= 1+(n-1)*2n
3. 9 is a factor of 10^n+1+3*10^n+5
Partial Fraction Decomposition
1. 3x^3+11x^2+16x+5
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x(x+1)^3
2. 2x^4-2x^3+6x^2-5x+1
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x^3-x^2+x-1