tính B=1+1/√1+1/√2+1/√3+...+1/√35
tính nhanh
a, 4/5 * 3/7 + 4/5 * 4/7
b, 20 * 45 + 55 * 20/35 * 1996 - 1991 * 35
c, (1 - 1/2) * (1 - 1/3) * (1 - 1/4) * (1 - 1/5)
a) 4/5 x 3/7 + 4/5 x 4/7
= 4/5 x ( 3/7 + 4/7 )
= 4/5 x 1
= 4/5
a) 4/5 x ( 3/7 + 4/7 )
= 4/5 x 1
= 4/5
b) 20 x 45 + 55 x 20 : 35 x 1996 - 1991 x 35
= 20 x ( 45 + 55 ) : 35 x ( 1996 - 1991 )
= 20 x 100 : 35 x 5
= 5 x 4 x 100 : 35 x 5
= 5 x 400 : 35 x 5
= \(\frac{5\cdot400}{35\cdot5}\Rightarrow=\frac{400}{35}.\)
1 Tính nhanh:
a. 1/15+1/35+1/63+1/99+1/143
b. 1/2+1/14+1/35+1/65+1/104+1/152
2 Chứng minh: D=(1/2)^2 +(1/3)^2 +(1/4)^2 +....+(1/10)^2 bé hơn 1
1: tính bằng cách hợp lí
a. 5/6 + 2/3 + 1/6
b: 13/35 + 2/7 + 12/35
c. 1/9 + 2/5 + 1/3 + 3/10
nhóm các số có cùng mẫu với nhau rồi cộng ra
Tính hợp lí:
A= -2/9 + -3/4 + 3/5 + 1/15 + 1/57 + 1/3 + -1/36
B= 1/2 + (-1/5 )+ (-5/7) + 1/6 + (-3/35) + 1/3 + 1/41
\(A=\frac{-2}{9}+\frac{-3}{4}+\frac{3}{5}+\frac{1}{15}+\frac{1}{57}+\frac{1}{3}+\frac{-1}{36}\)
\(A=\left(\frac{-2}{9}+\frac{-3}{4}+\frac{1}{3}+\frac{-1}{36}\right)+\left(\frac{3}{5}+\frac{1}{15}\right)+\frac{1}{57}\)
\(A=\left(\frac{-8}{36}+\frac{-27}{36}+\frac{12}{36}+\frac{-1}{36}\right)+\left(\frac{9}{15}+\frac{1}{15}\right)+\frac{1}{57}\)
\(A=\frac{-2}{3}+\frac{2}{3}+\frac{1}{57}\)
\(A=\frac{-38}{57}+\frac{38}{57}+\frac{1}{57}\)
\(A=\frac{1}{57}\)
Tính:
a) C = 3/1.3 + 3/3.5 + 3/3.7 +...+ 3/49.51
b) D = 1/2 + 1/14 + 1/35 + 1/65 + 1/104 + 1/152
a; C = \(\dfrac{3}{1.3}\) + \(\dfrac{3}{3.5}\) + \(\dfrac{3}{3.7}\) + ... + \(\dfrac{3}{49.51}\)
C = \(\dfrac{3}{2}\).(\(\dfrac{2}{1.3}\) + \(\dfrac{2}{3.5}\) + \(\dfrac{2}{5.7}\) + ... + \(\dfrac{2}{49.51}\))
C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{3}\) + \(\dfrac{1}{3}\) - \(\dfrac{1}{5}\) + \(\dfrac{1}{5}\) - \(\dfrac{1}{7}\) + ... + \(\dfrac{1}{49}\) - \(\dfrac{1}{51}\))
C = \(\dfrac{3}{2}\).(\(\dfrac{1}{1}\) - \(\dfrac{1}{51}\))
C = \(\dfrac{3}{2}\).\(\dfrac{50}{51}\)
C = \(\dfrac{25}{17}\)
Bài 1: cho A = 1 + 21 + 22 + 23 + ...... + 22007
a)Tính 2.A
b)Chứng minh A = 22006 - 1
Bài 2: cho A = 1 + 3 + 31 + 32 + 33 + 34 + 35 + 36 + 37
a)Tính 2.A
b)Chứng minh A = (38 - 1) : 2
Bài 3: cho B = 1 + 3 + 32 + ..... + 32006
a)Tính 3.B
b)Chứng minh B = (32007 - 1) : 2
Bài 4: cho C = 1 + 4 + 42 + 43 + 45 + 46
a)Tính 4.C
b)Chứng minh C = (47 - 1) : 3
Bài 5: Tính tổng
S = 1+ 2+ 22+ 23 + ...... + 22017
1.
a.\(A=1+2^1+2^2+2^3+...+2^{2007}\)
\(2A=2+2^2+2^3+....+2^{2008}\)
b. \(A=\left(2+2^2+2^3+...+2^{2008}\right)-\left(1+2^1+2^2+..+2^{2007}\right)\)
\(=2^{2008}-1\) (bạn xem lại đề)
2.
\(A=1+3+3^1+3^2+...+3^7\)
a. \(2A=2+2.3+2.3^2+...+2.3^7\)
b.\(3A=3+3^2+3^3+...+3^8\)
\(2A=3^8-1\)
\(=>A=\dfrac{2^8-1}{2}\)
3
.\(B=1+3+3^2+..+3^{2006}\)
a. \(3B=3+3^2+3^3+...+3^{2007}\)
b. \(3B-B=2^{2007}-1\)
\(B=\dfrac{2^{2007}-1}{2}\)
4.
Sửa: \(C=1+4+4^2+4^3+4^4+4^5+4^6\)
a.\(4C=4+4^2+4^3+4^4+4^5+4^6+4^7\)
b.\(4C-C=4^7-1\)
\(C=\dfrac{4^7-1}{3}\)
5.
\(S=1+2+2^2+2^3+...+2^{2017}\)
\(2S=2+2^2+2^3+2^4+...+2^{2018}\)
\(S=2^{2018}-1\)
4:
a:Sửa đề: C=1+4+4^2+4^3+4^4+4^5+4^6
=>4*C=4+4^2+...+4^7
b: 4*C=4+4^2+...+4^7
C=1+4+...+4^6
=>3C=4^7-1
=>\(C=\dfrac{4^7-1}{3}\)
5:
2S=2+2^2+2^3+...+2^2018
=>2S-S=2^2018-1
=>S=2^2018-1
Bài 5: Tính bằng cách thuận tiện nhất ; câu b tất cả là hỗn số
a) 2/3 : 3/5 x 5/7 : 2/3 + 2023 b) 1,1/2 x 1, 1/3 x 1, 1/8 x 1,1/15 x 1, 1/24 x 1, 1/35
a) 2/3 : 3/5 × 5/7 : 2/3
= 2/3 × 5/3 × 5/7 × 3/2
= 25/21
b) 1 1/2 × 1 1/3 × 1 1/18 × 1 1/15 × 1 1/24 × 1 1/35
= 3/2 × 4/3 × 19/18 × 16/15 × 25/24 × 36/35
= 2 × 152/35 × 15/14
= 304/35 × 15/14
= 152/7
Tính hợp lí :
A = \(\dfrac{-2}{9}\) + \(\dfrac{-3}{4}\) + \(\dfrac{3}{5}\) + \(\dfrac{1}{15}\) + \(\dfrac{1}{57}\) + \(\dfrac{1}{3}\) + \(\dfrac{-1}{36}\)
B = \(\dfrac{1}{2}\) + \(\dfrac{-1}{5}\) + \(\dfrac{-5}{7}\) + \(\dfrac{1}{6}\) + \(\dfrac{-3}{35}\) + \(\dfrac{1}{3}\) + \(\dfrac{1}{41}\)
C = \(\dfrac{-1}{2}\) + \(\dfrac{3}{5}\) + \(\dfrac{-1}{9}\) + \(\dfrac{1}{127}\) + \(\dfrac{-7}{18}\) + \(\dfrac{4}{35}\) + \(\dfrac{2}{7}\)
tính tổng 100 só đầu tiên
a)1/3 ; 1/15 ; 1/35;...
b) 1/2.4; 1/ 4.6 ; 1/6.8;..
2
a )Tìm tích 30 số dầu tiên
1 và 1/3; 1 và1/8 ;1 và 1/ 15 ; 1vaf 1/24 ; 1 và 1/35
b) rút gọn
a= ( 1 -1/3).(1 -1/6).(1 -1/9).(1 -1/15)....( 1 -1/190)
Ta có: 1/3 ; 1/15 ; 1/35;...
<=> 1/1.3 ; 1/3.5 ; 1/5.7
=> chữ số thứ 100 là: 1/199.201
Ta có: \(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{199.201}\)
\(=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+.....+\frac{1}{199}-\frac{1}{201}\)
\(=1-\frac{1}{201}=\frac{200}{201}\)
Giúp em ạ: Tính tổng: a) S = 1 + 3/2 + 2 + 5/2 + ... + 4039/2 + 2020 b) S = 1/3 + 1 + 5/3 + 7/3 + 3 + ... + 101/3 + 103/3 + 35
a: S=1+2+...+2020+(3/2+5/2+...+4039/2)
Đặt A=1+2+...+2020
Số số hạng là 2020-1+1=2020(số)
A=2020*(2020+1)/2=2041210
Đặt B=3/2+5/2+...+4039/2
Số số hạng là (4039-3):2+1=2019(số)
Tổng là (4039/2+3/2)*2019/2=2040199,5
=>S=2041210+2040199,5=4081409,5
b: S=1/3+3/3+5/3+...+101/3+103/3+105/3
Số số hạng là (105-1):2+1=104:2+1=53(số)
Tổng là (105/3+1/3)*53/2=106/3*53/2=2809/3