\(=1+\frac{1}{3}+1+\frac{1}{15}+...+1+\frac{1}{399}.\)
\(=10+\frac{1}{1.3}+\frac{1}{3.5}+...+\frac{1}{19.21}\)
=\(10+\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{19}-\frac{1}{21}\right)\)
=\(10+\frac{1}{2}\left(1-\frac{1}{21}\right)=10+\frac{1}{2}.\frac{20}{21}=\frac{220}{21}\)
Cho M=\(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{399}{400}\).Chứng minh rằng: M>18
cho M = \(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+\frac{24}{25}+...+\frac{399}{400}.\)
a> chứng tỏ M > 8
b> chứng tỏ M < 9
ai nhanh mình tick
\(\frac{4^2}{15}.\frac{5^2}{24}.\frac{6^2}{35}.....\frac{20^2}{399}\) tính nhanh
Tính nhanh A = \(\frac{2}{3}+\frac{2}{15}+\frac{2}{35}+...+\frac{2}{399}\)
Cho A = \(\frac{3}{4}+\frac{8}{9}+\frac{15}{16}+...+\frac{399}{400}\).
Chứng tỏ rằng A > 18
Tính : \(\frac{3}{4}.\frac{8}{9}.\frac{15}{16}.\frac{24}{25}.\frac{35}{36}.\frac{48}{49}.\frac{63}{64}\)
TÍNH \(\frac{4}{3}+\frac{16}{15}+\frac{36}{35}+...+\frac{2500}{249\cdot9}\)
Tính tổng 98 số đầu tiên của dãy số sau :
\(\frac{4}{3};\frac{9}{8};\frac{16}{15};\frac{25}{24};\frac{36}{35};...........\)