Tinh C= (5-1).(5+1).(5^2+1).(5^4+1).....(5^16+1)
tinh hop li:
a) 1+2+3...+20
b)1+3+5+...+21
c)2+5+8+...+2018 +2021
d)1*2+2*3+3*4+...+15*16
e)1*2*3+2*3*4+3*4*5+... +13*14*!5
Thuc hien phep tinh
A, 3/7 + 1/2 - (-3)/70
B, 3/5 + -1/25 - 35/100
C, 5/12 - 3/-16 + 3/4
D, 5/15 + 4/-12 + 1/7 - 1/-6
a,3/7 +1/2-[-3]/70
=13/14 -[-3]/70
=65/70 -[-3]/70
=34/35
b,3/5+-1/25 -35/100
=14/25 - 35/100
=56 /100 -35/100
= 21/100
c ,5/12 -3/-16+3/4
=29/48 +3/4
= 29/48 +36/48
=65/48
d, 5/15 +4/-12 +1/7 -1/-6
= 1/3 +1/-3 +1/7-1/-6
=0+1/7-1/-6
= 13/42
A.\(\dfrac{3}{7}+\dfrac{1}{2}+\dfrac{\left(-3\right)}{70}\)
=\([\dfrac{30}{70}+\dfrac{\left(-3\right)}{70}]\)+\(\dfrac{1}{2}\)
= \(\dfrac{27}{70}+\dfrac{35}{70}\)
=\(\dfrac{62}{70}=\dfrac{31}{35}\)
B.\(\dfrac{3}{5}+\dfrac{-1}{25}-\dfrac{35}{100}\)
=\(\dfrac{60}{100}+\dfrac{-4}{100}-\dfrac{35}{100}\)
=\(\dfrac{60+\left(-4\right)-35}{100}\)
=\(\dfrac{21}{100}\)
C.\(\dfrac{5}{12}-\dfrac{3}{-16}+\dfrac{3}{4}\)
=\(\left(\dfrac{5}{12}+\dfrac{9}{12}\right)-\dfrac{-3}{16}\)
=\(\dfrac{7}{6}-\dfrac{-3}{16}\)
=\(\dfrac{56}{48}-\dfrac{-9}{48}\)=\(\dfrac{65}{48}\)
D.\(\dfrac{5}{15}+\dfrac{4}{-12}+\dfrac{1}{7}-\dfrac{1}{-6}\)
=\(\dfrac{1}{3}+\dfrac{1}{7}+(\dfrac{-2}{6}-\dfrac{-1}{6})\)
=\(\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{-1}{6}\)
=\((\dfrac{1}{3}+\dfrac{-1}{6})+\dfrac{1}{7}\)
=\(\dfrac{1}{6}+\dfrac{1}{7}\)=\(\dfrac{13}{42}\)
a) 5/6 x 11/4 - 5/4 x 23/6
b) 9/16 x 13/4 - 9/4 x 5/16 + 9/16 x 17/
hay tinh tong:
1/1 x 2 + 1/2 x 3 + 1/3 x 4 + .... + 1/n (n + 1)
chung minh:
1/22 + 1/32 + 1/42 + ..... + 1/n2 < 1
giai dum nhe
Tinh nhanh
5/11+1/2+2/5+6/11+3/4+16/25+5/16
1313/2121+165/165/424242/151515
1/2+1/4+1/8+1/16+1/32+1/64+1/128+1/256
TINH TONG :
A/5+10+15+...+1500
B/ 5+8+11+...+155
C/1+2+4+8+16+...+1024
D/ 0+1+4+9+16+...+10000
E/ 0+1+8+27+...+3375
A/5+10+15+...+1500
=5+10+15+...+1500 ta có:1500-5:5+1=300(số hạng)
=(5+1500)x300:2=225750
tính
a/ 3 và 1/2 - 4/5 - 8 và 1/2 -1/5 -(2021)^0
b/ 32^5/ 16^5 - (0.2)^100 * (5)^100 -√8181 + /-21/
c/ 3/2* 16/21 + 3/2 * 5/21 - (- 1/10) ^0 - /-20/
c: \(=\dfrac{3}{2}\cdot1-1-20=\dfrac{3}{2}-21=\dfrac{-39}{2}\)
rút gon: C=12(5^2+1)(5^4+1)(5^8+1)(5^16+1)
\(C=12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\frac{1}{2}\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\frac{1}{2}\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\frac{1}{2}\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
\(=\frac{1}{2}\left(5^{16}-1\right)\left(5^{16}+1\right)\)
\(=\frac{1}{2}\left(5^{32}-1\right)\)
\(=\frac{5^{32}-1}{2}\)
Thuc hien phep tinh sau bang cach hop li nhat:
a)5/11+1/2+2/5+6/11+3/4+16/25+5/16
b)19/4+37/100+1/8+132/25+5/2+37/12
5/11+1/2+2/5+6/11+3/4+16/25+5/16
=1441/400
19/4+37/100+1/8+132/25+5/2+37/12
=1933/120
Ban lam sao duooc nhu the giai ra cho minh voi
12(52+1)(54+1)(58+1)(516+1)
=\(\frac{1}{2}\)(52−1)(52+1)(54+1)(58+1)(516+1)
=\(\frac{1}{2}\)(54−1)(54+1)(58+1)(516+1)
=\(\frac{1}{2}\)(58−1)(58+1)(516+1)
=\(\frac{1}{2}\)(516−1)(516+1)
=\(\frac{1}{2}\)(532−1)
phép trên thuộc 7 hđt mở rộng nhá (sử dụng hđt 3 bằng phương pháp trung hồi )
các bạn chỉ cần gải thích cho mình phép trên sao lại có \(\frac{1}{2}\)là đc rồi (làm như thế nào)
12
= \(\frac{24}{2}\)
= \(\frac{1}{2}\left(25-1\right)\)
= \(\frac{1}{2}\left(5^2-1\right)\)
Chép đề sai kìa