rút gọn A= 1+5+5^2+...+5^50
ai giúp mik vs
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NN
1
22 tháng 9 2020
Ta có:
\(P=\frac{\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(P=\frac{\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(P=\frac{\left(5^8-1\right)\left(5^8+1\right)\left(5^{16}+1\right)}{2}\)
\(P=\frac{\left(5^{16}-1\right)\left(5^{16}+1\right)}{2}\)
\(P=\frac{5^{32}-1}{2}\)
mình trình bày trong hình, hơi mờ bạn thông cảm!
20 tháng 8 2020
\(\left[\frac{\sqrt{5}\left(1+\sqrt{5}\right)}{\sqrt{5}}+\frac{\sqrt{2}\left(\sqrt{2}-1\right)}{1-\sqrt{2}}\right].\frac{\sqrt{2}+\sqrt{5}}{1}=1+\left(\sqrt{5}-\sqrt{2}\right)\left(\sqrt{2}+\sqrt{5}\right)=1+3=4\)
P
1
17 tháng 8 2018
a)\(4\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(=\dfrac{1}{2}.\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(=\dfrac{1}{2}.\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\)
\(=\dfrac{1}{2}.\left(3^8-1\right)\left(3^8+1\right)\)
\(=\dfrac{1}{2}.\left(3^{16}-1\right)\)
\(=\dfrac{1}{2}3^{16}-\dfrac{1}{2}\)
b) \(48\left(5^2+1\right)\left(5^4+1\right).....\left(5^{32}+1\right)\)
\(=2.\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right).....\left(5^{32}+1\right)\)
\(=2.\left(5^4-1\right)\left(5^4+1\right).....\left(5^{32}+1\right)\)
\(=2.\left(5^8+1\right).....\left(5^{32}+1\right)\)
\(=2.\left(5^{32}-1\right)\)
\(=2.5^{32}-2\)
Tham khảo nhé~
LP
3
MT
3 tháng 2 2017
(a+b)2-(a-b)2=[(a+b)+(a-b)][(a+b)-(a-b)]=(a+b+a-b)(a+b-a+b)=2a.2b=4ab
1 tháng 8 2016
a)
\(A=\frac{6^3+3.6^3+3^3}{-13}=\frac{3^3.2^3+3^3.2^2+3^3}{-13}=\frac{3^3\left(8+4+1\right)}{-13}=\frac{27.13}{-13}=-27\)
b)
A=1+5+52+53+...+550
5A=5+52+53+...551
5A-A=(5+52+53+...+551)-(1+5+52+...+550)
4A=551-1
A=\(\frac{5^{51}-1}{4}\)
c)
A=2100-299+298-...+22-2
2A=2101-2100+299-...+23-22
2A+A=(2101-2100+...+23-22)+(2100-299+...+22-2)
3A=2101-2
A=\(\frac{2^{101}-2}{3}\)
TN
1 tháng 8 2016
b.
\(A=1+5+5^2+5^3+...+5^{49}+5^{50}\)
\(5A=5+5^2+5^3+...+5^{50}+5^{51}\)
\(5A-A=\left(5+5^2+5^3+...+5^{50}+5^{51}\right)-\left(1+5+5^2+..+5^{50}\right)\)
\(4A=5^{51}-1\)
\(A=\frac{5^{51}-1}{4}\)
MN
1
2 tháng 8 2018
Ta có:
\(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=\left(x-3\right)^3-\left(x-3\right)^3+6\left(x+1\right)^2\)
\(=6\left(x+1\right)^2\)
A=1+5+52+53+...+550
=> 5A=(5+52+53+...+550)+551
=> 5A-A=551-1
4A=551-1 => \(A=\frac{5^{51}-1}{4}\)
cảm ơn bạn nhé