giải giúp : 1/2.3 + 1/3.4 + 1/4.5+ … + 1/9.10 15/08/2021 Bởi Josie giải giúp : 1/2.3 + 1/3.4 + 1/4.5+ … + 1/9.10
1/2.3 + 1/3.4 + 1/4.5+ … + 1/9.10 = 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/9 – 1/10 = 1/2 – 1/10 = 5/10 – 1/10 = 4/10 = 2/5 Bình luận
Đáp án: \(\frac{2}{5}\) Giải thích các bước giải: \(\begin{array}{l}\frac{1}{{2.3}} + \frac{1}{{3.4}} + \frac{1}{{4.5}} + … + \frac{1}{{9.10}}\\ = \frac{{3 – 2}}{{2.3}} + \frac{{4 – 3}}{{3.4}} + \frac{{5 – 4}}{{4.5}} + … + \frac{{10 – 9}}{{9.10}}\\ = \frac{1}{2} – \frac{1}{3} + \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + … + \frac{1}{9} – \frac{1}{{10}}\\ = \frac{1}{2} – \frac{1}{{10}}\\ = \frac{2}{5}\end{array}\) Bình luận
1/2.3 + 1/3.4 + 1/4.5+ … + 1/9.10
= 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + … + 1/9 – 1/10
= 1/2 – 1/10
= 5/10 – 1/10
= 4/10 = 2/5
Đáp án:
\(\frac{2}{5}\)
Giải thích các bước giải:
\(\begin{array}{l}
\frac{1}{{2.3}} + \frac{1}{{3.4}} + \frac{1}{{4.5}} + … + \frac{1}{{9.10}}\\
= \frac{{3 – 2}}{{2.3}} + \frac{{4 – 3}}{{3.4}} + \frac{{5 – 4}}{{4.5}} + … + \frac{{10 – 9}}{{9.10}}\\
= \frac{1}{2} – \frac{1}{3} + \frac{1}{3} – \frac{1}{4} + \frac{1}{4} – \frac{1}{5} + … + \frac{1}{9} – \frac{1}{{10}}\\
= \frac{1}{2} – \frac{1}{{10}}\\
= \frac{2}{5}
\end{array}\)