Question

Cho C=1/3x4/6x7/9x....x208/210 chung minh rang C<1/25

Answer 1

Ta có:
C=\(\dfrac{1}{3}.\dfrac{4}{6}.\dfrac{7}{9}..........\dfrac{208}{210}\)<\(\dfrac{1}{3}.\dfrac{3}{4}.\dfrac{6}{7}.......\dfrac{207}{208}\)

\(\Rightarrow\)C²<\(\dfrac{1}{3}.\dfrac{4}{6}.\dfrac{7}{9}..........\dfrac{208}{210}\).\(\dfrac{1}{3}.\dfrac{3}{4}.\dfrac{6}{7}.......\dfrac{207}{208}\)

\(\Rightarrow\)C²<\(\dfrac{1.4.7........208}{3.6.9........210}\).\(\dfrac{1.3.6.9........207}{3.4.7........208}\)

\(\Rightarrow\)C²<\(\dfrac{1}{210}.\dfrac{1}{3}\)=\(\dfrac{1}{630}< \dfrac{1}{625}\)

\(\Rightarrow\)C<\(\dfrac{1}{25}\)(đpcm)