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\(a)\) \(S=1+2+2^2+2^3+...+2^{2017}\)
\(2S=2+2^2+2^3+2^4+...+2^{2018}\)
\(2S-S=\left(2+2^2+2^3+2^4+...+2^{2018}\right)-\left(1+2+2^2+2^3+...+2^{2017}\right)\)
\(S=2^{2018}-1\)
\(b)\) \(S=3+3^2+3^3+...+3^{2017}\)
\(3S=3^2+3^3+3^4+...+3^{2018}\)
\(3S-S=\left(3^2+3^3+3^4+...+3^{2018}\right)-\left(3+3^2+3^3+...+3^{2017}\right)\)
\(2S=3^{2018}-3\)
\(S=\frac{3^{2018}-3}{2}\)
\(c)\) \(S=4+4^2+4^3+...+4^{2017}\)
\(4S=4^2+4^3+4^4+...+4^{2018}\)
\(4S-S=\left(4^2+4^3+4^4+...+4^{2018}\right)-\left(4+4^2+4^3+...+4^{2017}\right)\)
\(3S=4^{2018}-4\)
\(S=\frac{4^{2018}-4}{3}\)
\(d)\) \(S=5+5^2+5^3+...+5^{2017}\)
\(5S=5^2+5^3+5^4+...+5^{2018}\)
\(5S-S=\left(5^2+5^3+5^4+...+5^{2018}\right)-\left(5+5^2+5^3+...+5^{2017}\right)\)
\(4S=5^{2018}-5\)
\(S=\frac{5^{2018}-5}{2}\)
Chúc em học tốt ~
S= 3/5.7 + 3/7.9 +...........................+3/59.61
=3/2.(1/5 - 1/7 +1/7 -1/9 +....................+ 1/59-1/61)
=3/2.(1/5-1/61)
mình chỉ làm được tới đó
\(T=\dfrac{3}{5\cdot7}+\dfrac{3}{7\cdot9}+\dfrac{3}{9\cdot11}+...+\dfrac{3}{59\cdot61}\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{2}{5\cdot7}+\dfrac{2}{7\cdot9}+\dfrac{2}{9\cdot11}+...+\dfrac{2}{59\cdot61}\right)\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+...+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}\cdot\left(\dfrac{1}{5}-\dfrac{1}{61}\right)=\dfrac{3}{2}\cdot\dfrac{56}{305}=\dfrac{84}{305}\)
\(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{59.61}\)
\(=3.\left(\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+...+\dfrac{1}{59.61}\right)\)
\(=3.\dfrac{1}{2}.\left(\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+....+\dfrac{1}{59}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\left(\dfrac{1}{5}-\dfrac{1}{61}\right)\)
\(=\dfrac{3}{2}.\dfrac{56}{305}\)
\(=\dfrac{84}{305}\)
a.
\(M=1.\left[\frac{1}{3}-\frac{1}{5}+.....\frac{1}{97}-\frac{1}{99}\right]\)
\(M=\frac{1}{3}-\frac{1}{99}=\frac{32}{99}\)
b.
\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{197}-\frac{1}{199}\right]\)
\(N=\frac{3}{2}.\left[\frac{1}{5}-\frac{1}{199}\right]=\frac{291}{995}\)
mk đầu tiên nha bạn
a, \(5S=5^2+5^3+...+5^{2017}\)
\(5S-S=5^{2017}-5\)
\(S=\frac{5^{2017}-5}{4}\)
b,\(3S=3^2+3^3+...+3^{101}\)
\(3S-S=3^{101}-3\)
\(S=\frac{3^{101}-3}{2}\)
c, \(3S=3-3^2+3^3-...-3^{2016}\)
\(3S+S=1-3^{2016}\)
\(4S=1-3^{2016}\)
\(S=\frac{1-3^{2016}}{4}\)
b, 3S = 3^2+3^3+.....+3^101
2S=3S-S=(3^3+3^3+.....+3^101)-(3+3^2+....+3^100) = 3^101-3
=> S = (3^101-3)/2
Tk mk nha
biểu thức trên =\(\frac{1}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.....+\frac{1}{56}-\frac{1}{61}\right)=\frac{1}{2}\left(\frac{1}{5}-\frac{1}{61}\right)=\frac{1}{2}x\frac{61}{305}=\frac{1}{10}=0,1.\)
vậy biểu thức trên =0,1
\(S=1^2+2^2+3^2+...+56^2\)
\(=1.2-1+2.3-2+3.4-3+...+56.57-56\)
\(=\left(1.2+2.3+3.4+...+56.57\right)-\left(1+2+3+...+56\right)\)
\(=\frac{56.57.58}{3}-\frac{56.57}{2}=\frac{2.56.57.58}{6}-\frac{3.56.57}{6}\)
\(=\frac{2.56.57.58-3.56.57}{6}=\frac{56.57.\left[2.58-3\right]}{6}\)
\(=\frac{56.57.\left(2.56+1\right)}{6}=\frac{56.57.113}{6}=60116\)
Ta thấy \(\sqrt{60116}\notin N\Rightarrow\)\(S\) không phải là số chính phương.
ai k mình k lại [ chỉ 3 người đầu tiên mà trên 10 điểm hỏi đáp ]
S = 3/3.5 + 3/7.9 +3/9.11 +...+ 3/59.61
S = 3/2 . (2/5.7 + 2/7.9 + 2/9.11 + ... + 2/59.61)
S = 3/2 . (1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... +1/59 - 1/61)
S = 3/2 . (1/5 - 1/61)
S = 3/2 . 56/305
S = 84/305
VẬY ĐÁP ÁN LÀ B NHA