\(B=1+5+5^2+5^3+...+5^{2008}+5^{2009}\)
Đặt \(5B=5.\text{ (}1+5+5^2+5^3+...+5^{2008}+5^{2009}\text{)}\)
\(\Rightarrow5B=5+5^2+5^3+...+5^{2009}+5^{2010}\)
\(\Rightarrow5B-B=\left(5+5^2+5^3+...+5^{2009}+5^{2010}\right)-\left(1+5+5^2+...+5^{2009}\right)\)\(\Rightarrow4B=5^{2010}-1\)
\(\Rightarrow B=\dfrac{5^{2010}-1}{4}\)
Vậy \(B=\dfrac{5^{2010}-1}{4}\)
=1+5+52+53+...+52008+52009
Tính hợp lý:
a, \(2008\cdot\left(\dfrac{1}{2007}-\dfrac{2009}{1004}\right)-2009\cdot\left(\dfrac{1}{2007}-2\right)\)
b,\(\dfrac{5^5\cdot20^3-5^4\cdot20^3+5^7\cdot4^5}{\left(20+5\right)^3\cdot4^5}\)
tính hợp lý :
a, \(2008.\left(\dfrac{1}{2007}-\dfrac{2009}{1004}\right)-2009.\left(\dfrac{1}{2007}-2\right)\)
b, \(\dfrac{5^5.20^3-5^4.20^3+5^7.4^5}{\left(20+5\right)^3.4^5}\)
a, Tính tổng A = 1 + 5 + 52 + 53 + ... + 52008 + 52009
b, B = 2100 \(-\) 299 + 298 \(-\) 297 + ... + 22
c, C = ( 1000 - 13 ) . ( 1000 - 23 ) . (1000 - 33 ) ... ( 1000 - 503)
B = 1 + 5 + 52 + 53 + ....... + 52008 + 52009
S = 1 + 2 + 5 + 14 + ....... + 3n-1 + 1/2 (với n thuộc Z)
A = 1 + 3/2^3 + 4/2^4 + 5/2^5 + ...... + 100/2^100
Q = 1 + 1/2*(1+2) + 1/3*(1+2+3) + 1/4*(1+2+3+4) + ...... + 1/20*(1+2+3+.....+20)
M = -4/1*5 - 4/5*9 - 4/9*13 - ....... - 4/(n+4)*n
Giúp mk với! Mk đang cần gấp lắm !!!!!
\(\left|3x-5\right|=2009\left(2010^{2009}+2010^{2008}+...+2010+1\right)-2010^{2010}+5\)
CMR :1/5+1/13+1/25+1/2008^2+2009^2<1/2
Tính tổng B=1+5+52+......+52009
1. tìm x,y,z biết
a. 8x=5y,7y=12z và x+y+z= -318
b. \(\dfrac{5z-6y}{4}=\dfrac{6x-4z}{5}=\dfrac{4y-5x}{6}\)và 3x-2y+5z=96
c. 2009-|x-2009|=x
d. \(\left(2x-1\right)^{2008}\)+\(\left(y-\dfrac{2^{ }}{5}\right)^{2008}\)+|x+y-z|=0
