__4__ + __4__ + __4__ + ………___4__ 3*5 5*7 7*9 99 *101 31/08/2021 Bởi Reese __4__ + __4__ + __4__ + ………___4__ 3*5 5*7 7*9 99 *101
.\(\begin{array}{l}\frac{4}{{3 \times 5}} + \frac{4}{{5 \times 7}} + \frac{4}{{7 \times 9}} + … + \frac{4}{{99 \times 101}}\\ = \frac{1}{2} \times 4 \times \left( {\frac{1}{3} – \frac{1}{5} + \frac{1}{5} – \frac{1}{7} + \frac{1}{7} – \frac{1}{9} + …. + \frac{1}{{99}} – \frac{1}{{101}}} \right)\\ = 2 \times \left( {\frac{1}{3} – \frac{1}{{101}}} \right)\\ = 2 \times \frac{{98}}{{303}}\\ = \frac{{196}}{{303}}\end{array}\). Bình luận
Đáp án: A = $\frac{196}{303}$ Giải thích các bước giải: A = $\frac{1}{2}$ (($\frac{4}{3}$ – $\frac{4}{5}$ ) + ($\frac{4}{5}$ – $\frac{4}{7}$ ) + (($\frac{4}{7}$ – $\frac{4}{9}$ )) + ….. + ($\frac{4}{99}$ – $\frac{4}{101}$ ) A = $\frac{1}{2}$ (($\frac{4}{3}$ – $\frac{4}{101}$ )) A= $\frac{1}{2}$ $\frac{392}{303}$ A = $\frac{196}{303}$ Bình luận
.\(\begin{array}{l}\frac{4}{{3 \times 5}} + \frac{4}{{5 \times 7}} + \frac{4}{{7 \times 9}} + … + \frac{4}{{99 \times 101}}\\ = \frac{1}{2} \times 4 \times \left( {\frac{1}{3} – \frac{1}{5} + \frac{1}{5} – \frac{1}{7} + \frac{1}{7} – \frac{1}{9} + …. + \frac{1}{{99}} – \frac{1}{{101}}} \right)\\ = 2 \times \left( {\frac{1}{3} – \frac{1}{{101}}} \right)\\ = 2 \times \frac{{98}}{{303}}\\ = \frac{{196}}{{303}}\end{array}\).
Đáp án:
A = $\frac{196}{303}$
Giải thích các bước giải:
A = $\frac{1}{2}$ (($\frac{4}{3}$ – $\frac{4}{5}$ ) + ($\frac{4}{5}$ – $\frac{4}{7}$ ) + (($\frac{4}{7}$ – $\frac{4}{9}$ )) + ….. + ($\frac{4}{99}$ – $\frac{4}{101}$ )
A = $\frac{1}{2}$ (($\frac{4}{3}$ – $\frac{4}{101}$ ))
A= $\frac{1}{2}$ $\frac{392}{303}$
A = $\frac{196}{303}$