${B}$=$\frac{1}{2.4.6}$+$\frac{1}{4.6.8}$+......+ $\frac{1}{46.48.50}$
${4B}$=${4}$ . ( $\frac{1}{2.4.6}$+$\frac{1}{4.6.8}$+......+ $\frac{1}{46.48.50}$)
${4B}$=$\frac{4}{2.4.6}$+$\frac{4}{4.6.8}$+......+ $\frac{4}{46.48.50}$
Số hạng tổng quát của ${4B}$ là:
$\frac{4}{n(n+2)(n+4)}$ ( ${n}$ ∈ ${N*}$)
=$\frac{(n+4)-n}{n(n+2)(n+4)}$
=$\frac{(n+4)}{n(n+2)(n+4)}$ - $\frac{n}{n(n+2)(n+4)}$
=$\frac{1}{n(n+2}$ - $\frac{n}{(n+2)(n+4)}$
Khi đó:
${4B}$= ( $\frac{1}{2.4}$ - $\frac{1}{4.6}$ ) + ( $\frac{1}{4.6}$ - $\frac{1}{6.8}$ )+.....+ ( $\frac{1}{46.48}$ - $\frac{1}{48.50}$ )
${4B}$= $\frac{1}{2.4}$ - $\frac{1}{4.6}$ + $\frac{1}{4.6}$ - $\frac{1}{6.8}$ +.....+ $\frac{1}{46.48}$ - $\frac{1}{48.50}$
${4B}$= $\frac{1}{2.4}$ - $\frac{1}{48.50}$
${B}$= $\frac{1}{2.4.4}$ - $\frac{1}{48.50.4}$
${B}$= $\frac{1}{32}$ - $\frac{1}{9600}$
${B}$= $\frac{299}{9600}$
CHÚC EM HỌC TỐT!! :))
