1. tính nhanh tổng sau :
1/6+ 1/18+ 1/36+ 1/60+ 1/90+ 1/126
Tính A
A=1/6 + 1/18 + 1/36 + 1/60 + 1/90 + 1/126
\(3A=\frac{3}{2.3}+\frac{3}{6.3}+\frac{1}{12.3}+\frac{3}{20.3}+\frac{3}{30.3}+\frac{3}{42.3}\)
\(3A=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
\(3A=\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)
\(3A=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{6}-\frac{1}{7}\)
\(3A=1-\frac{1}{7}=\frac{6}{7}\Rightarrow A=\frac{2}{7}\)
tính; 1/6+ 1/18 +1/60+ 1/90 +1/126
Hình như bạn viết thiếu \(\frac{1}{36}\), nếu đúng là vậy thì mình giải như sau.
Đặt A =\(\frac{1}{6}+\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+\frac{1}{90}+\frac{1}{126}\)
3A = \(\frac{3}{3.2}+\frac{3}{3.6}+\frac{3}{3.12}+\frac{3}{3.20}+\frac{3}{3.30}+\frac{3}{3.42}\)
3A = \(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\)
3A = \(\frac{2-1}{1.2}+\frac{3-2}{2.3}+\frac{4-3}{3.4}+...+\frac{7-6}{6.7}\)
3A = \(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{6}-\frac{1}{7}\)
3A = \(1-\frac{1}{7}=\frac{6}{7}\)
A = \(\frac{6}{7}:3=\frac{2}{7}\)
Gọi tổng là A:
ta có :
3A= 1/2+1/6+1/20+1/30+1/42
3A= 1/1.2+1/2.3+1/4.5+1/6.7
3A= 1-1/2+1/2-1/3+1/4-1/5+1/6-1/7
3A=1-1/3+1/4-1/5+1/6-1/7
3A= (1-1/7)+(1/3-1/4)+(1/5-1/7)
3A=6/7+-1/12+-2/35
3A=6/7-2/35+-1/12
3A=4/5-1/12
3A=43/60
A=43/180
\(A=\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+\frac{1}{90}+\frac{1}{126}+\frac{1}{168}\)
\(A=\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+...+\frac{1}{168}\)
\(\frac{1}{3}A=\frac{1}{54}+\frac{1}{108}+...+\frac{1}{504}\)
\(\frac{1}{3}A=\frac{1}{6.9}+\frac{1}{9.12}+...+\frac{1}{21.24}\)
\(=\frac{1}{6}-\frac{1}{9}+\frac{1}{9}-\frac{1}{12}+...+\frac{1}{21}-\frac{1}{24}\)
\(=\frac{1}{6}-\frac{1}{24}\)
\(=\frac{4-1}{24}=\frac{3}{24}=\frac{1}{8}\)
=> \(A=\frac{1}{8}:\frac{1}{3}\)\(=\frac{3}{8}\)
1/6+1/18+1/60+1/90+1/126
\(\frac{1}{6}\)+\(\frac{1}{18}\)+\(\frac{1}{36}\)+\(\frac{1}{60}\)+\(\frac{1}{90}\)\(\frac{1}{126}\)
=1/2.3+1/3.6+1/6.6+1/6.10+1/10.9+1/9.14
=1/2-1/3+1/3-1/6+1/6-1/6+1/6-1/10+1/10-1/9+1/9-1/14
=1/2-1/14
=6/14=3/7
\(\frac{1}{6}+\frac{1}{18}+\frac{1}{36}+\frac{1}{60}+\frac{1}{90}+\frac{1}{126}\)
\(=\frac{1}{2\cdot3}+\frac{1}{3\cdot6}+\frac{1}{6\cdot6}+\frac{1}{6\cdot10}+\frac{1}{10\cdot9}+\frac{1}{9\cdot14}\)
\(=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{6}+\frac{1}{6}-\frac{1}{6}+\frac{1}{6}-\frac{1}{10}+\frac{1}{10}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}\)
\(=\frac{1}{2}-\frac{1}{14}\)
\(=\frac{3}{7}\)
A= 1/6 + 1/18 + 1/36 + 1/60 + 1/90.
CHO MÌNH CÁCH GIẢI VỚI Ạ BẠN MẶC THIÊN PHONG ƠI. MÌNH CẢM ƠN
A= 1/6 + 1/18 + 1/36 + 1/60 + 1/90
= 1/3(1/2+1/6+1/12+1/20+1/30)
=1/3(1/1x2+1/2x3+1/3x4+1/4x5+1/5x6)
=1/3(1-1/2+1/2-1/3+...+1/5-1/6)
=1/3(1-1/6)
=1/3x5/6
=5/18
Vậy giá trị biểu thức A là 5/18
a. Tính tổng
1+2+3+4+5+6+7+8+9+10
b. Áp dụng câu a để tính nhanh tổng sau
9+18+27+36+45+54+63+72+81+90
a. =(1+10)×10 :2
=11×10:2
=110:2
=55
b. Số các số hạng là =(90-9):9+1= 10
Tổng = (9+90)×10:2=495
BÀI 1: XÉT XEM CÁC TỔNG HAY HIỆU SAU CÓ CHIA HẾT CHO 6 KHÔNG :
1/.66-16 2/.18+36+72+49 3/.12+36+24+18+3+51 4/.7+150-90+17+18 5/.126+120+23+5
Tính nhanh:
a,1/4+2/5+6/8+9/15+8/1
b,1/2+2/4+3/6+4/8+5/10+6/12+7/14+8/16+9/18+10/20
c,1/10+4/20+9/30+16/40+25/50+36/60+49/70+64/80+81/90