How can I solve this by using the principle of mathematical induction? How can I prove that [math]2^{k+1} < 1+(k+1) *2^k[/math] for k=1, 2, 3, 4...?
How can I solve this problem [math]\dfrac{2}{3}(k+2) +\dfrac{1}{4}(k-4)=k-\dfrac{1}{6}[/math]?