\(\frac{31}{2}\)\(.\)\(\frac{32}{2}\)\(.\)\(\frac{33}{2}\)\(....\)\(\frac{60}{2}\)

\(=\)\(\left[\left(31.32.33....60\right)\right]\)\(.\)\(\left(\frac{1.2.3....30}{2^{30}}\right)\)\(.\)\(\left(1.2.3....30\right)\)

\(=\)\(\left[\frac{\left(1.3.5....59\right).\left(2.4.6....60\right)}{2.4.6....60}\right]\)\(=\)\(1.3.5....59\)

Vậy \(\frac{31}{2}\)\(.\)\(\frac{32}{2}\)\(.\)\(\frac{33}{2}\)\(....\)\(\frac{60}{2}\)\(=\)\(1.3.5....59\)

ta có:Đặt A= \(1.3.5.....59=\frac{1.2.3.4.....59.60}{2.4.6.....60}\)

=\(\frac{1.2.3.....59.60}{2^{30}.\left(1.2.3.....30\right)}=\frac{31.32.....59.60}{2^{30}}\)

= \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)

vì \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\) = \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)    

\(\Rightarrow\)A= \(\frac{31}{2}.\frac{32}{2}.....\frac{59}{2}.\frac{60}{2}\)

                                          ( Điều phải chứng minh)

toán nâng cao lớp 6 đấy bạn nha

sửu nhi

:>

chọn câu nào thì giải thích giúp mik luôn nha

\(60!=1\cdot2\cdot3\cdot4\cdot5\cdot...\cdot59\cdot60=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2\cdot4\cdot6\cdot...\cdot58\cdot60\)

\(=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\cdot1\cdot2\cdot3\cdot...\cdot30=1\cdot3\cdot5\cdot...\cdot57\cdot59\times2^{30}\times30!\)

\(\Rightarrow1\cdot3\cdot5\cdot...\cdot59=\frac{60!}{30!\times2^{30}}=\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}\)đpcm.

\(\frac{31}{2}\cdot\frac{32}{2}\cdot...\cdot\frac{60}{2}\cdot2\cdot4\cdot...\cdot58\cdot60\)

=31.32.33.34...60.1.2.3.4.5...29.30

=1.2.3.4.5.6.7.8.9.10...60

1.3.5.7...59.2.4.6.8...60

=1.2.3.4.5.6...60

Vậy \(\frac{31}{2}\cdot\frac{32}{2}\cdot\frac{33}{2}\cdot...\cdot\frac{60}{2}=1\cdot3\cdot5\cdot...\cdot59\)

\(1.3.5....59=\frac{\left(1.3.5....59\right).\left(2.4.6....60\right)}{2.4.6....60}=\frac{\left(1.2.3.4.5...30\right).31....59.60}{2^{30}.\left(1.2.3...30\right)}=\frac{31.32....60}{2^{30}}=\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}\)

Chị quản lý Sao làm tốt thế mà chẳng được olm công nhận nhỉ

Vì đó là người quản lí nên công nhận cũng có được gì !!!

Ta có: \(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=\frac{31.32.33...60}{2.2.2...2}=\frac{31.32.33...60}{2^{30}}\)

                                                       (30 số 2)

\(=\frac{\left(31.32.33...60\right).\left(1.2.3...30\right)}{2^{30}.\left(1.2.3...30\right)}=\frac{31.32.33...60.1.2.3...30}{\left(2.1\right).\left(2.2\right).\left(2.3\right)...\left(2.30\right)}=\frac{\left(1.3.5...59\right).\left(2.4.6...60\right)}{\left(2.4.6...60\right)}=1.3.5...59\)

\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=\frac{31.32.33...60}{2^{30}}\)

\(=\frac{\left(31.32.33...60\right).\left(1.2.3...30\right)}{2^{30}.\left(1.2.3...30\right)}\)

\(=\frac{1.2.3...60}{2^{30}\left(1.2.3...30\right)}\)

\(=\frac{\left(1.3.5.7...59\right)\left(2.4.6.8...60\right)}{\left(2.4.6.8...60\right)}\)

\(=1.3.5.7...59\)

Ta có:

31/2.32/2.33/2....60/2=31.32......60/2^30

=(31.32.33....60)(1.2.3....30)/2^30(1.2.3...30)

=(1.3.5...59)(2.4.6...60)/(2.4.6...60)=1.3.5...59

=>P=Q

nhớ ****

cái dòng 3, 4 mk ko hiểu sao 2^30.(1.2.3....30) lại bằng 2.4.6...60

ak hểu r

Ta có:

\(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=\frac{31.32.33...60}{2^{30}}\)

                                    \(=\frac{\left(31.32.33...60\right).\left(1.2.3...30\right)}{2^{30}.\left(1.2.3...30\right)}\)

                                    \(=\frac{1.2.3...60}{2^{30}\left(1.2.3...30\right)}\)

                                    \(=\frac{\left(1.3.5.7...59\right)\left(2.4.6.8...60\right)}{\left(2.4.6.8...60\right)}\)

                                    \(=1.3.5.7...59\)

Vậy \(\frac{31}{2}.\frac{32}{2}.\frac{33}{2}...\frac{60}{2}=1.3.5.7...59\)