=1/1-1/4+1/4-1/7+....+1/n-1/n+3
=1-1/n+3
=n+2/n+3
Ta có :
3/ 1.4 + 3/ 4.7 + 3/ 7.10 + ... + 3/ n( n + 1 )
= 1 - 1/4 + 1/4 - 1/7 + ... + 1/ n - 1/ n + 3 .
= 1 - 1/ n+3 .
= n+3 - 1 / n+3
= n+2 / n+3 .
\(3.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+...+\frac{1}{n.\left(n+3\right)}\right)\)
\(3.\left(1.\frac{1}{4}+\frac{1}{4}.\frac{1}{7}+\frac{1}{7}.\frac{1}{10}+...+\frac{1}{n}.\frac{1}{n+3}\right)\)
\(3.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\right)\)
\(3.\left(1-\frac{1}{n+3}\right)=3.\frac{n+2}{n+3}=\frac{6n+6}{n+3}\)
3/1.4 + 3/4.7 + 3/7.10 + ... + 3/n.(n+3)
=1-1/4+1/4-1/7+1/7-1/10+....+1/n -1/n+3
=1 - 1/ n+3
=n+3/n+3 - 1/n+3
= n+2/n+3
\(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+...+\frac{3}{n\left(n+3\right)}\)
\(=1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+...+\frac{1}{n}-\frac{1}{n+3}\)
\(=1-\frac{1}{n+3}\)
\(=\frac{n+2}{n+3}\)
_Chúc bạn học tốt_
