(1+2/4)*(1+2/10)*(1+2/18)*…….*((n+1)*(n+2))/(n*(n+3)) 14/08/2021 Bởi Kylie (1+2/4)*(1+2/10)*(1+2/18)*…….*((n+1)*(n+2))/(n*(n+3))
Đáp án: 1+24)(1+210)(1+218)...(n+1)(n+2)n(n+3)=64.1210.2018...(n+1)(n+2)n(n+3)=2.31.4.3.42.5.4.53.6...(n+1)(n+2)n(n+3)=2.3.4…(n+1)1.2.3…n.3.4.5…(n+2)4.5.6…(n+3)=(n+1).3(n+3)=3(n+1)n+3 Giải thích các bước giải:1+24)(1+210)(1+218)...(n+1)(n+2)n(n+3)=64.1210.2018...(n+1)(n+2)n(n+3)=2.31.4.3.42.5.4.53.6...(n+1)(n+2)n(n+3)=2.3.4…(n+1)1.2.3…n.3.4.5…(n+2)4.5.6…(n+3)=(n+1).3(n+3)=3(n+1)n+3 Bình luận
Đáp án: \(\frac{{3(n + 1)}}{{n + 3}}\) Giải thích các bước giải: \(\begin{array}{l}(1 + \frac{2}{4})(1 + \frac{2}{{10}})(1 + \frac{2}{{18}})…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\ = \frac{6}{4}.\frac{{12}}{{10}}.\frac{{20}}{{18}}…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\ = \frac{{2.3}}{{1.4}}.\frac{{3.4}}{{2.5}}.\frac{{4.5}}{{3.6}}…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\ = \frac{{2.3.4…(n + 1)}}{{1.2.3…n}}.\frac{{3.4.5…(n + 2)}}{{4.5.6…(n + 3)}}\\ = (n + 1).\frac{3}{{(n + 3)}}\\ = \frac{{3(n + 1)}}{{n + 3}}\end{array}\) Bình luận
Đáp án:
1+24)(1+210)(1+218)...(n+1)(n+2)n(n+3)=64.1210.2018...(n+1)(n+2)n(n+3)=2.31.4.3.42.5.4.53.6...(n+1)(n+2)n(n+3)=2.3.4…(n+1)1.2.3…n.3.4.5…(n+2)4.5.6…(n+3)=(n+1).3(n+3)=3(n+1)n+3
Giải thích các bước giải:1+24)(1+210)(1+218)...(n+1)(n+2)n(n+3)=64.1210.2018...(n+1)(n+2)n(n+3)=2.31.4.3.42.5.4.53.6...(n+1)(n+2)n(n+3)=2.3.4…(n+1)1.2.3…n.3.4.5…(n+2)4.5.6…(n+3)=(n+1).3(n+3)=3(n+1)n+3
Đáp án:
\(\frac{{3(n + 1)}}{{n + 3}}\)
Giải thích các bước giải:
\(\begin{array}{l}
(1 + \frac{2}{4})(1 + \frac{2}{{10}})(1 + \frac{2}{{18}})…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\
= \frac{6}{4}.\frac{{12}}{{10}}.\frac{{20}}{{18}}…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\
= \frac{{2.3}}{{1.4}}.\frac{{3.4}}{{2.5}}.\frac{{4.5}}{{3.6}}…\frac{{(n + 1)(n + 2)}}{{n(n + 3)}}\\
= \frac{{2.3.4…(n + 1)}}{{1.2.3…n}}.\frac{{3.4.5…(n + 2)}}{{4.5.6…(n + 3)}}\\
= (n + 1).\frac{3}{{(n + 3)}}\\
= \frac{{3(n + 1)}}{{n + 3}}
\end{array}\)