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\(\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}+\left(\frac{1}{3}-\frac{1}{3}\right)+\left(\frac{1}{4}-\frac{1}{4}\right)+\left(\frac{1}{5}-\frac{1}{5}\right)-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}\)
\(=\frac{1}{3}\)
a) 25 + 69 + 75 + 11
= (25 + 75) + (69 + 11)
= 100 + 80
= 180
b) 64 x 867 + 36 x 867
= (64 + 36) x 867
= 100 x 867
= 86700
c) 25 x 989 x 4 + 25
= 25 x 4 x 989 + 25
= 100 x 989 + 25
= 98900 + 25
= 98925
\(A=\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+...+\frac{1}{972}+\frac{1}{2916}\)
\(3A=\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+...+\frac{1}{324}+\frac{1}{972}\)
\(3A-A=\left(\frac{3}{4}+\frac{1}{4}+\frac{1}{12}+...+\frac{1}{324}+\frac{1}{972}\right)-\left(\frac{1}{4}+\frac{1}{12}+\frac{1}{36}+...+\frac{1}{972}+\frac{1}{2916}\right)\)
\(2A=\frac{3}{4}-\frac{1}{2916}\)
\(A=\frac{1093}{2916}\)
\((\frac{3}{5}+\frac{2}{5})+(\frac{4}{7}+\frac{1}{7}+\frac{2}{7})\) ) =1+1=2
=(1/9+1/3)+(2/5+3/10) =(1/9+3/9)+(4/10+3/10) =4/9+7/10 =40/90+63/90 =103/90
A=14+112+136+...+1972+12916
3A=34+14+112+...+1324+1972
3A−A=(34+14+112+...+1324+1972)−(14+112+136+...+1972+12916)
2A=34−12916
A=10932916
