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\(B=7-7^4+7^7-....+7^{301}\)
\(\Leftrightarrow7^3B=7^4-7^7+7^{10}+......+7^{304}\)
\(\Leftrightarrow7^3B-B=\left(7^4-7^7+7^{10}+...+7^{304}\right)-\left(7-7^4+...+7^{301}\right)\)
\(\Leftrightarrow342B=7^{304}-7\)
\(\Leftrightarrow\frac{7^{304}-7}{342}\)
trường sai nhé
\(B=7-7^4+7^7-7^{10}+...+7^{301}\)
\(\Rightarrow7^3B=7^4-7^7+7^{10}-7^{13}+...+7^{302}\)
\(\Rightarrow7^3B+B=\left(7^4-7^7+7^{10}-7^{13}+...+7^{302}\right)+\left(7-7^4+7^{10}-7^{13}+....+7^{301}\right)\)
\(\Rightarrow344B=7^{302}+7-7^{301}\)
\(\Rightarrow B=\frac{7^{302}+7-7^{301}}{344}\)
7^3 . 9 + 7^3 . 7^4 - 45 . 539
= 343 .9 + 343 . 2401 - 45 . 539
= 343 . (9 + 2401) - 45 . 539
= 343 . 2410 - 24255
= 826630 - 24255
= 802375
73B=74-77+710-...-7301+7304
73B-B=(74-77+710-...-7301+7304)-(7-74+77-...+7301)
343B-B=74-77+710-...-7301+7304-7+74-77+...-7301
342B=7304-7
B=\(\frac{7^{304}-7}{342}\)
B = 7-74+77-.....-7300+7301
73B = 74-77+710-....-7301+7302
344B = 73B + B = 7 + 7302
=> B = \(\frac{7+7^{302}}{344}\)
\(A=1+5^2+5^4+...+5^{200}\)
\(5^2A=5^2+5^4+5^6+...+5^{202}\)
\(25A-A=\left(5^2+5^4+5^6+...+5^{202}\right)-\left(1+5^2+5^4+...+5^{200}\right)\)
\(24A=5^{202}-1\)
\(A=\frac{5^{202}-1}{24}\)
Câu B có sai đề ko vậy
\(b,\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-81^2\right)\)
\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left[3^8-\left(3^4\right)^2\right]\)
\(=\left(1^2+2^3+3^4+4^5\right).\left(1^3+2^3+3^3+4^3\right).\left(3^8-3^8\right)\)
\(=\left(1^2+2^3+3^4+4^5\right)\left(1^3+2^3+3^3+4^3\right).0=0\)
a, = 71995 . ( 72 - 1) : 71995 = 49 - 1 = 48
b, = ........... x ( 38 - 38) = 0
Đặt A=7-74+77-...+7301
73A=74-77+710-...+7303
343A-A=74-77+710-...+7303-(7-74+77-...+7301)
344A=7303-7
A= (7303-7)/344