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2. Prove that if n > 1, then 1(1!) + 2(2!) + ... + n(n!) = (n + 1)! - 1.
3. Given that AH =-622.2kJ N,H., +02: H4+503, »N,, +24,0, H40, AH =-285.8kJ Determine the heat of reaction for: N2g +2H,, ->N,H41 Is the reaction endothermic or exothermic?
22.M. If c>0 and n is a natural number, there exists a unique positive number b such that b" = c.
11. Let an >0 and assume that bn = n+1 + B. What can we say about the convergence of an? an
5. Evaluate the limit: lim expn n! n>00
Prove that is an integer for all n > 0.
5. Prove that U(2") (n > 3) is not cyclic.
Construct a PDA that accepts {a"ba" bn | n0Am >0};
Prove by mathematical induction (discrete mathematics)
n? - 2*n-1 > 0 n> 3
2. Suppose that X Binom(n,p) such that n>1 and 0 <p<1. Show that E[(x + 1)-1 = _(1 – p)p+1 – 1 p(n + 1)