B1: a)(1-1/2).(1-1/3).(1-1/4)...(1-1/2025 b) 1/2.5+1/5.8+...+1/17.20 B2: (11/12+11/12.23+11/23.34+...+11/89.100).x+1/25=-2/15

B1: a) $(1-\frac{1}{2})\times (1-\frac{1}{3})\times (1-\frac{1}{4})\times ...\times (1-\frac{1}{2025})$ $=\frac{1}{2}\times \frac{2}{3}\times \frac{3}{4}\times ...\times \frac{2024}{2025}$ $=\frac{1\times 2\times 3\times ...\times 2024}{2\times 3\times 4\times ...\times 2025}$ $=\frac{1}{2025}$ b) $\frac{1}{2\times 5}+\frac{1}{5\times 8}+...+\frac{1}{17\times 20}$ $=\frac{1}{3}\times (\frac{3}{2\times 5}+\frac{3}{5\times 8}+...+\frac{3}{17\times 20})$ $=\frac{1}{3}\times (1-\frac{1}{5}+\frac{1}{5}-\frac{1}{8}+...+\frac{1}{17}-\frac{1}{20})$ $=\frac{1}{3}\times (1-\frac{1}{20})$ $=\frac{1}{3}\times \frac{19}{20}$ $=\frac{19}{60}$ B2: $(\frac{11}{12}+\frac{11}{12\times 23}+\frac{11}{23\times 34}+...+\frac{11}{89\times 100})\times x+\frac{1}{25}=-\frac{2}{15}$ $(\frac{11}{12}+\frac{11}{12\times 23}+\frac{11}{23\times 34}+...+\frac{11}{89\times 100})\times x=-\frac{2}{15}-\frac{1}{25}$ $(\frac{11}{12}+\frac{11}{12\times 23}+\frac{11}{23\times 34}+...+\frac{11}{89\times 100})\times x=-\frac{13}{75}$ $\frac{11}{12}\times (1+\frac{1}{23}+\frac{1}{34}+...+\frac{1}{100})\times x=-\frac{13}{75}$ $\frac{11}{12}\times (\frac{23-12}{12\times 23}+\frac{34-23}{23\times 34}+...+\frac{100-89}{89\times 100})\times x=-\frac{13}{75}$ $\frac{11}{12}\times (\frac{1}{12}-\frac{1}{23}+\frac{1}{23}-\frac{1}{34}+...+\frac{1}{89}-\frac{1}{100})\times x=-\frac{13}{75}$ $\frac{11}{12}\times (\frac{1}{12}-\frac{1}{100})\times x=-\frac{13}{75}$ $\frac{11}{12}\times \frac{19}{12\times 100}\times x=-\frac{13}{75}$ $\frac{209}{14400}\times x=-\frac{13}{75}$ $x=-\frac{13}{75}:\frac{209}{14400}$ $x=-\frac{13}{75}\times \frac{14400}{209}$ $x=-\frac{1248}{209}$