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\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
\( \begin{array}{l} \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{6} +\frac{1}{12} +\frac{1}{20} +...+\frac{1}{240}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2.3} +\frac{1}{3.4} +\frac{1}{4.5} +...+\frac{1}{15.16}\right)\\ \Leftrightarrow B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{3} +\frac{1}{3} -\frac{1}{4} +...+\frac{1}{15} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\left(\frac{1}{2} -\frac{1}{16}\right)\\ \Leftrightarrow \ B=\frac{1}{2} .\frac{7}{16}\\ \Leftrightarrow \ B=\frac{7}{32} \end{array}\)
a) 2 x 12 x 43 + 3 x 32 x 8 + 25 x 6 x4
=(2 x12) x43+(3 x8) x32+(6 x4) x25
=24 x43+24 x32+ 24 x25
=24 x(43+32+25)
=24 x100
=2400
b) 78 x 31 + 78 x 24 + 17 x 78 + 28 x 78
=78x(31+24+17+28)
=78x100
=7800
9x24+25=9x24+24.1+1
=24x(9+1)+1
=24x10+1
=240+1=241
9x24 + 25
= 9 x 24 +24 x 1 + 1
= 24 x ( 9 + 1) + 1
= 24 x 10 + 1
= 240 + 1 = 241