Bài 1 tính tổng
A= \(\frac{15}{90.94}\)+ \(\frac{15}{94.98}\) +........+ \(\frac{15}{146.150}\)
B=\(\frac{6}{15.18}\)+ \(\frac{6}{18.21}\)+ ..........+\(\frac{6}{87.90}\)
Giải chi tiết giúp mình với nha!
A=7/10.11+7/11.12+7/12.13+...+7/69.70. B=6/15.18+6/18.21+...+6/87.90
C=15/90.94+15/94.98+...+15/146.150. D=10/56+10/140+10/260+...+10/140
Tính
\(G=\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)
k mình nha mấy bạn mình bị âm quá trời quá đất lun nè hu..............huhu
Đăng bài gì mà dễ thế! tớ lớp 5 giải còn được đấy! Ai thấy tớ đúng thì tk nha
A=\(\frac{15}{90.94}+\frac{15}{94.98}+.....+\frac{15}{146.150}\)
\(A=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146.150}\)
\(A=15\left(\frac{1}{90.94}+\frac{1}{94.98}+...+\frac{1}{146.150}\right)\)
\(A=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(A=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{150}\right)\)
\(A=\frac{15}{4}.\frac{1}{225}\)
\(A=\frac{1}{60}\)
\(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+.....+\frac{15}{146.150}\)
\(\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)
\(=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{150}\right)\)
\(=\frac{15}{4}.\frac{1}{225}\)
\(=\frac{1}{60}\)
\(\frac{15}{90\cdot94}+\frac{15}{94\cdot98}+\frac{15}{98\cdot102}+...+\frac{15}{146\cdot150}\)
\(=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{150}\right)\)
\(=\frac{15}{4}\cdot\frac{1}{225}=\frac{1}{60}\)
a)(ghi lại đề)
=\(\frac{15}{4}\)x( \(\frac{4}{90}\)x 94+\(\frac{4}{94}\) x 98+...+\(\frac{4}{146}\)x150)
=15/4 x[(1/90 -1/94)+(1/94-1/98)+...+1/146-1/150)]
=15/4x (1/90-1/150)
=15/4 x 2/2450
=1/60
(Lúc đầu siêng nên ghi dài còn lúc sau lười r , k hỉu thj hỏi)
bài 3: chứng tỏ rằng:
b) Đặt A = \(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}
Ta có: \(A=\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\)
\(=\frac{1}{3}(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90})\)
\(=\frac{1}{3}(\frac{1}{15}-\frac{1}{90})\)
\(=\frac{1}{3}(\frac{6}{90}-\frac{1}{90})\)
\(=\frac{1}{3}.\frac{5}{90}\)
\(=\frac{1}{54}\)
Ta có: 1= \(\frac{54}{54}\)
Suy ra A < 1 (đpcm)
3A=3*(1/15*18+1/18*21+...+1/87*90)
3A=3/15*18+3/18*21+...+3/87*90
3A=1/15-1/18+1/18-1/21+...+1/87-1/90
3A=1/15-1/90
3A=1/18
A=1/18 chia3
A=1/54
vì 1/54<1 nên A<1
1) Tính bằng cách hợp lí (Tính nhanh)
a) \(A=\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98+102}+........+\frac{15}{146.150}\)
b) \(B=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+............+\frac{10}{1400}\)
Bạn nào làm được giúp mik, mik tick cko nha
* Tính tổng sau :
H = \(\frac{15}{90.94}\)+\(\frac{15}{94.98}\)+\(\frac{15}{98.102}\)+...+ \(\frac{15}{146.150}\).
Mình cần gấp. Mong các bạn giúp đỡ !!!
Bạn nào làm đúng và nhanh , mình sẽ tick nhé <3
Thanks :)
Ta có :
\(H=\frac{15}{90.94}+\frac{15}{94.98}+\frac{15}{98.102}+...+\frac{15}{146.150}\)
\(H=\frac{15}{4}\left(\frac{4}{90.94}+\frac{4}{94.98}+\frac{4}{98.102}+...+\frac{4}{146.150}\right)\)
\(H=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(H=\frac{15}{4}\left(\frac{1}{90}-\frac{1}{150}\right)\)
\(H=\frac{15}{4}.\frac{1}{225}\)
\(H=\frac{1}{60}\)
Vậy \(H=\frac{1}{60}\)
Chúc bạn học tốt ~
\(H=\frac{15}{90\cdot94}+\frac{15}{94\cdot98}+\frac{15}{98\cdot102}+...+\frac{15}{146\cdot150}\)
\(H=15\left(\frac{1}{90\cdot94}+\frac{1}{94\cdot98}+\frac{1}{98\cdot102}+...+\frac{1}{146\cdot150}\right)\)
\(H=15\left[\frac{1}{4}\left(\frac{4}{90\cdot94}+\frac{4}{94\cdot98}+\frac{4}{98\cdot102}+...+\frac{4}{146\cdot150}\right)\right]\)
\(H=15\left[\frac{1}{4}\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+\frac{1}{98}-\frac{1}{102}+...+\frac{1}{146}-\frac{1}{150}\right)\right]\)
\(H=15\left[\frac{1}{4}\left(\frac{1}{90}-\frac{1}{150}\right)\right]\)
\(H=15\left[\frac{1}{4}\cdot\frac{1}{225}\right]\)
\(H=15\cdot\frac{1}{900}\)
\(H=\frac{1}{60}\)
H = 15/90.94 + 15/94.98 + 15/98.102 + ... + 15/146.150
H = 15(1/90.94 + 1/94.98 + 1/98.102 + ... + 1/146.150)
H = 15/4 (4/90.94 + 4/94.98 + 4/98.102 + ... +4/146.150)
H = 15/4 ( 1/90 - 1/94 + 1/94 - 1/98 + 1/98 - 1/102 + ... + 1/146 - 1/150)
H = 15/4 (1/90 - 1/150)
H = 15/4 (5/450 - 3/450)
H = 15/4 . 1/225
H = 1/60
Tính hợp lí
\(A=\left(\frac{21}{31}+\frac{-16}{7}\right)+\left(\frac{44}{53}+\frac{10}{21}\right)+\frac{9}{53}\)
\(B=\frac{6}{15.18}+\frac{6}{18.21}+...+\frac{6}{87.90}\)
\(A=\frac{21}{31}+\frac{-16}{7}+\frac{44}{53}+\frac{10}{21}+\frac{9}{53} \)
\(A=\left(\frac{16}{7}+\frac{10}{21}\right)+\left(\frac{44}{53}+\frac{9}{53}\right)+\frac{21}{31}\)
\(A=\frac{58}{21}+1+\frac{21}{31}\)
\(A=\frac{100}{21}\)
\(B=6\left(\frac{1}{15.18}+\frac{1}{18.21}+...+\frac{1}{87.90}\right)\)
\(B=6\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+...+\frac{1}{87}-\frac{1}{90}\right)\)
\(B=6\left(\frac{1}{15}-\frac{1}{90}\right)\)
\(B=6.\frac{1}{18}\)
\(B=\frac{1}{3}\)
\(E=\frac{1}{25.27}+\frac{1}{27.29}+...+\frac{1}{73.75}.\)
\(F=\frac{15}{90.94}+\frac{15}{94.98}+...+\frac{15}{146.150}\)
\(G=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
Bài 2
\(\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{100^2}.\)
CMR A<\(\frac{3}{4}\)
\(E=\frac{1}{25\cdot27}+\frac{1}{27\cdot29}+...+\frac{1}{73\cdot75}\)
\(E=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{27}+\frac{1}{27}-\frac{1}{29}+...+\frac{1}{73}-\frac{1}{75}\right)\)
\(\Rightarrow E=\frac{1}{2}\left(\frac{1}{25}-\frac{1}{75}\right)=\frac{1}{2}\cdot\frac{2}{75}=\frac{1}{75}\)
\(F=\frac{15}{90\cdot94}+\frac{15}{94\cdot98}+...+\frac{15}{146\cdot150}\)
\(F=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{94}+\frac{1}{94}-\frac{1}{98}+...+\frac{1}{146}-\frac{1}{150}\right)\)
\(\Rightarrow F=\frac{15}{4}\cdot\left(\frac{1}{90}-\frac{1}{150}\right)=\frac{15}{4}\cdot\frac{1}{225}=\frac{1}{60}\)
\(G=\frac{10}{56}+\frac{10}{140}+\frac{10}{260}+...+\frac{10}{1400}\)
\(G=\frac{5}{28}+\frac{5}{70}+\frac{5}{130}+...+\frac{5}{700}\)
\(G=\frac{5}{4\cdot7}+\frac{5}{7\cdot10}+\frac{5}{10\cdot13}+...+\frac{5}{25\cdot28}\)
\(G=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+...+\frac{1}{25}-\frac{1}{28}\right)\)
\(\Rightarrow G=\frac{5}{3}\left(\frac{1}{4}-\frac{1}{28}\right)=\frac{5}{3}\cdot\frac{3}{14}=\frac{5}{14}\)