Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(=5^{20}+\left(5^2\right)^{11}+\left(5^{ }^3\right)^7\)
=\(5^{^{ }20}+5^{22}+5^{21}\)
\(=5^{20}\cdot\left(1+5^2+5^1\right)\)
=\(5^{20}\cdot\left(1+25+5\right)\)
=\(5^{20}\cdot31\)
Vì 31 chia hết chó 31 nên
\(5^{20}+25^{^{ }11}+125^7\)chia hết cho 31
\(^{5^{20}+25^{11}+125^7}\)=\(1.5^{20}+25.25^{10}+\left(5^3\right)^7\)=\(1.5^{20}+25.\left(5^2\right)^{10}+5^{21}\)=\(1.5^{20}+25.5^{20}+5.5^{20}\)
=\(^{5^{20}.\left(1+25+5\right)}\)=\(5^{20}.31\)chia hết cho 31
Vậy \(5^{20}+25^{11}+125^7\)chia hết cho 31
P = 32 + 62 + 92 + ... + 302
P = 32 . (12 + 22 + 32 + ... + 102)
P = 9 . 385
P = 3465
a) C = 106 + 57
C = 26 . 56 + 57
C = 56 . (26 + 5)
C = 56 . (64 + 5)
C = 56 . 69 chia hết cho 69
b) 310 . 199 - 39 . 500
= 39 . (3.199 - 500)
= 39 . (597 - 500)
= 39 . 97 chia hết cho 97
Đặt \(A=\frac15+\frac{1}{13}+\frac{1}{25}+\cdots+\frac{1}{10^2+11^2}\)
\(=\frac15+\frac{1}{13}+\frac{1}{25}+\cdots+\frac{1}{100+121}\)
\(=\frac15+\frac{1}{13}+\frac{1}{25}+\cdots+\frac{1}{221}\)
=>\(A<\frac15+\frac{1}{12}+\frac{1}{24}+\cdots+\frac{1}{220}\)
=>\(A<\frac15+\frac12\left(\frac16+\frac{1}{12}+\cdots+\frac{1}{110}\right)\)
=>\(A<\frac15+\frac12\left(\frac12-\frac13+\frac13-\frac14+\cdots+\frac{1}{10}-\frac{1}{11}\right)\)
=>\(A<\frac15+\frac12\left(\frac12-\frac{1}{11}\right)=\frac15+\frac12\cdot\frac{9}{22}=\frac15+\frac{9}{44}\)
=>\(A<\frac{44}{220}+\frac{45}{220}=\frac{89}{220}\)
=>\(A<\frac{99}{220}=\frac{9}{20}\)