Question

9£®ÒÑÖªS_n£¬T_n·Ö±ðÊǵȲîÊýÁÐ{a_n}Óë{b_n}µÄÇ°nÏîºÍ£¬ÇÒ$\frac{S_n}{T_n}=\frac{2n+1}{4n-2}£¨n=1£¬2£¬¡­£©$£¬Ôò$\frac{{{a_{10}}}}{{{b_3}+{b_{18}}}}+\frac{{{a_{11}}}}{{{b_6}+{b_{15}}}}$=£¨¡¡¡¡£©

• A£® $\frac{11}{20}$
• B£® $\frac{41}{78}$
• C£® $\frac{43}{82}$
• D£® $\frac{23}{42}$

Answer 1

·ÖÎö ÓɵȲîÊýÁеÄÐÔÖÊ£¬Öª$\frac{{{a_{10}}}}{{{b_3}+{b_{18}}}}+\frac{{{a_{11}}}}{{{b_6}+{b_{15}}}}$=$\frac{{a}_{10}{+a}_{11}}{{b}_{10}{+b}_{11}}$=$\frac{{S}_{20}}{{T}_{20}}$£¬ÓÉ´ËÄܹ»Çó³ö½á¹û£®

½â´ð ½â£º¡ßS_n£¬T_n·Ö±ðÊǵȲîÊýÁÐ{a_n}£¬{b_n}µÄÇ°nÏîºÍ£¬
ÇÒ$\frac{S_n}{T_n}=\frac{2n+1}{4n-2}£¨n=1£¬2£¬¡­£©$£¬£¨n¡ÊN₊£©£¬
¡à$\frac{{{a_{10}}}}{{{b_3}+{b_{18}}}}+\frac{{{a_{11}}}}{{{b_6}+{b_{15}}}}$=$\frac{{a}_{10}{+a}_{11}}{{b}_{10}{+b}_{11}}$=$\frac{{S}_{20}}{{T}_{20}}$=$\frac{40+1}{80-2}$=$\frac{41}{78}$£¬
¹ÊÑ¡£ºB£®

µãÆÀ ±¾Ì⿼²éµÈ²îÊýÁеÄͨÏʽºÍÇ°nÏîºÍ¹«Ê½µÄÓ¦Ó㬽âÌâʱҪÈÏÕæÉóÌ⣬×Ðϸ½â´ð£¬×¢ÒâºÏÀíµØ½øÐеȼÛת»¯£®