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\(A=5+5^2+5^3+5^4+...+5^{39}+5^{40}\)
\(=\left(5+5^2\right)+\left(5^3+5^4\right)+...+\left(5^{39}+5^{40}\right)\)
\(=5\left(1+5\right)+5^3\left(1+5\right)+...+5^{39}\left(1+5\right)\)
\(=6\left(5+5^3+...+5^{39}\right)⋮6\)
Suy ra \(A⋮3,A⋮2\).
\(S=1-5+5^2-5^3+...+5^{58}-5^{59}\)
\(5.S=5-5^2+5^3-5^4+...+5^{59}-5^{60}\)
\(5.S-S=1-5^{60}\)
\(4.S=1-5^{60}\)
\(S=\frac{1-5^{60}}{4}\)
Vậy\(S=\frac{1-5^{60}}{4}\)
\(A=\frac{4116-14}{10290}\)
\(A=\frac{14\times\left(294-1\right)}{735\times14}\)
\(A=\frac{294-1}{735}\)
\(A=\frac{293}{735}\)
Vậy A có giá trị \(\frac{293}{735}\)
\(B=\frac{2929-101}{2\times1919+404}\)
\(B=\frac{101\times\left(29-1\right)}{35\times\left(38+4\right)}\)
\(B=\frac{28}{42}\)
\(B=\frac{2}{3}\)
Vậy B có giá trị \(\frac{2}{3}\)
\(A=\frac{4116-14}{10290}\)
\(A=\frac{14.\left(294-1\right)}{735.14}\)
\(A=\frac{294-1}{735}\)
\(A=\frac{293}{735}\)
\(B=\frac{2929-101}{2.1919+404}\)
\(B=\frac{2828}{2.1919+2.202}\)
\(B=\frac{2.1414}{2.\left(1919+202\right)}\)
\(B=\frac{1414}{2121}\)
\(B=\frac{101.14}{101.21}\)
\(B=\frac{14}{21}\)
\(B=\frac{2}{3}\)
ta có: S= 1 + 5 + 5^2 + 5^3 + .......+ 5^2015
=> S=(1+5+5^2+5^3)+(5^4+5^4+5^6+5^7)+.........+(5^2012+5^2013+5^2014+5^2015)
=> S=1.(1+5+5^2+5^3)+5^4.(1+5+5^2+5^3)+..........+5^2012.(1+5+5^2+5^3)
=>S=1.156+5^4.156+.........+5^2012.156
=>S=156.(1+5^4+.......+5^2012)
=>S=13.12.(1+5^4+.......+5^2012) chia hết cho 13
vậy S chia hết cho 13. ( đpcm)
CHÚC CÁC BẠN HỌC GIỎI.
\(B=\frac{2929-101}{2.1919+404}\)
\(B=\frac{29.101-101}{38.101+4.101}\)
\(B=\frac{101.\left(29-1\right)}{101.\left(38+4\right)}\)
\(B=\frac{2}{3}\)
\(a,\dfrac{\left(-11\right).3+7.\left(-11\right)}{\left(-15\right).22}=\dfrac{\left(-11\right).\left(3+7\right)}{\left(-15\right).22}=\dfrac{-11.10}{-15.22}=\dfrac{-11.2.5}{-11.3.5+2.11}=\dfrac{-1}{-3}=\dfrac{1}{3}\\ \dfrac{25.11}{15.37-15.48}\\ =\dfrac{5.5.11}{15.\left(37-48\right)}=\dfrac{5.5.11}{15.\left(-11\right)}=\dfrac{5.5.11}{3.5.\left(-11\right)}=\dfrac{5}{-3}=-\dfrac{5}{3}\\ \dfrac{-2.3.5^2}{3^2.5^3}=\dfrac{-2}{3.5}=-\dfrac{2}{15}\)
