a) m = 5555/6666 -246246/369369 + 222222/151515 =
b) A= [ 1+1/2] x [1+1/3] x [1+1/4] x .......... x [1+1/99] =
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\(M=\frac{5555}{6666}-\frac{246246}{369369}+\frac{222222}{151515}\)
\(M=\frac{5}{6}-\frac{2}{3}+\frac{22}{15}\)
\(M=\frac{49}{30}\)
\(M=\frac{5555}{6666}-\frac{246246}{369369}+\frac{222222}{151515}=\frac{5}{6}-\frac{2}{3}+\frac{22}{15}=\frac{25}{30}-\frac{20}{30}+\frac{44}{30}=\frac{49}{30}\)
\(\frac{5555}{6666}\)= \(\frac{5}{6}\)
\(\frac{246246}{369369}\)= \(\frac{82}{123}\)
\(\frac{222222}{151515}\)= \(\frac{22}{15}\)
M= \(\frac{5}{6}\)+ \(\frac{82}{123}\)+ \(\frac{22}{15}\)
M= \(\frac{1025}{1230}\)+ \(\frac{820}{1230}\)+ \(\frac{6724}{1230}\)
M= \(\frac{1845}{1230}\)+ \(\frac{6724}{1230}\)
M= \(\frac{8569}{1230}\)
tk nhé
Bài 2:
\(\Leftrightarrow5a+14\in\left\{2;3;5;7;11;13;17;19;23;29;31;37\right\}\)
\(\Leftrightarrow5a\in\left\{5;15\right\}\)
hay a=3(vì a là số nguyên tố)
\(A=\frac{1}{2}×\frac{3}{4}+\frac{1}{4}×\frac{1}{2}\)
\(A=\frac{1}{2}×\left(\frac{3}{4}+\frac{1}{4}\right)\)
\(A=\frac{1}{2}×\left(\frac{3+1}{4}\right)\)
\(A=\frac{1}{2}×1\)
\(A=\frac{1}{2}\)
\(B=\frac{1212}{2121}×\frac{151515}{161616}\)
\(B=\frac{1212:101}{2121:101}×\frac{151515:10101}{161616:10101}\)
\(B=\frac{12}{21}×\frac{15}{16}\)
\(B=\frac{12×15}{21×16}\)
\(B=\frac{3×4×3×5}{3×7×4×4}\)
\(B=\frac{15}{28}\)