Question

va rog urgent dau coroana ​

Answer 1

$S=\frac{2-1}{1\cdot 2}+\frac{3-2}{3\cdot 2}+...+\frac{100-99}{99\cdot 100}\\ \\ S=\frac{2}{1\cdot 2}-\frac{1}{1\cdot 2}+\frac{3}{3\cdot 2}-\frac{2}{3\cdot 2}+...+\frac{100}{99\cdot 100}-\frac{99}{99\cdot 100}\\ \\ S=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}...-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}\\ \\S=\frac{1}{1}-\frac{1}{100}=\frac{100}{100}-\frac{1}{100}\\ \\ =\frac{99}{100}<1; \ (99<100)$