Tính B=3+33+35+...+31991
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NT
3
OY
24 tháng 10 2021
Tham khảo
https://hoc24.vn/cau-hoi/c-3-33-35-31991-chia-het-cho-13-va-41.2492703297984
24 tháng 10 2021
\(A=\left(3+3^2+3^3\right)+\left(3^4+3^5+3^6\right)+...+\left(3^{1989}+3^{1990}+3^{1991}\right)\\ A=3\left(1+3+3^2\right)+3^4\left(1+3+3^2\right)+...+3^{1989}\left(1+3+3^2\right)\\ A=\left(1+3+3^2\right)\left(3+3^4+...+3^{1989}\right)\\ A=13\left(3+3^4+...+3^{1989}\right)⋮13\)
K
1
22 tháng 10 2021
\(C=\left(3+3^3+3^5\right)+\left(3^7+3^9+3^{11}\right)+...+\left(3^{1987}+3^{1989}+3^{1991}\right)\\ C=\left(3+3^3+3^5\right)+3^6\left(3+3^3+3^5\right)+...+3^{1986}\left(3+3^3+3^5\right)\\ C=\left(3+3^3+3^5\right)\left(1+3^6+...+3^{1986}\right)\\ C=273\left(1+3^6+...+3^{1986}\right)\\ C=13\cdot21\left(1+3^6+...+3^{1986}\right)⋮13\\ C=\left(3+3^3+3^5+3^7\right)+\left(3^9+3^{11}+3^{13}+3^{15}\right)+...+\left(3^{1985}+3^{1987}+3^{1989}+3^{1991}\right)\\ C=\left(3+3^3+3^5+3^7\right)+3^8\left(3+3^3+3^5+3^7\right)+...+3^{1984}\left(3+3^3+3^5+3^7\right)\\ C=\left(3+3^3+3^5+3^7\right)\left(1+3^8+...+3^{1984}\right)\\ C=2460\left(1+3^8+...+3^{1984}\right)\\ C=41\cdot60\left(1+3^8+...+3^{1984}\right)⋮41\)
10 tháng 10 2021
\(B=2+2^2+2^3+...+2^{60}\)
\(=2\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)
\(=7\cdot\left(2+...+2^{58}\right)⋮7\)
KV
23 tháng 12 2023
A = 8⁸ + 2²⁰
= (2³)⁸ + 2²⁰
= 2²⁴ + 2²⁰
= 2²⁰.(2⁴ + 1)
= 2²⁰.17 ⋮ 17
Vậy A ⋮ 17
21 tháng 10 2023
a: \(G=8^8+2^{20}\)
\(=2^{24}+2^{20}\)
\(=2^{20}\left(2^4+1\right)=2^{20}\cdot17⋮17\)
b: Sửa đề: \(H=2+2^2+2^3+...+2^{60}\)
\(=2\left(1+2\right)+2^3\left(1+2\right)+...+2^{59}\left(1+2\right)\)
\(=3\left(2+2^3+...+2^{59}\right)⋮3\)
\(H=2+2^2+2^3+...+2^{60}\)
\(=2\left(1+2+2^2\right)+2^4\left(1+2+2^2\right)+...+2^{58}\left(1+2+2^2\right)\)
\(=7\left(2+2^4+...+2^{58}\right)⋮7\)
\(H=2+2^2+2^3+...+2^{60}\)
\(=\left(2+2^2+2^3+2^4\right)+...+\left(2^{57}+2^{58}+2^{59}+2^{60}\right)\)
\(=2\left(1+2+2^2+2^3\right)+...+2^{57}\left(1+2+2^2+2^3\right)\)
\(=15\left(2+2^5+...+2^{57}\right)⋮15\)
c: \(E=\left(1+3+3^2\right)+3^3\left(1+3+3^2\right)+...+3^{1989}\left(1+3+3^2\right)\)
\(=13\left(1+3^3+...+3^{1989}\right)⋮13\)
\(E=1+3+3^2+3^3+...+3^{1991}\)
\(=\left(1+3+3^2+3^3+3^4+3^5\right)+\left(3^6+3^7+3^8+3^9+3^{10}+3^{11}\right)+...+3^{1986}+3^{1987}+3^{1988}+3^{1989}+3^{1990}+3^{1991}\)
\(=364\left(1+3^6+...+3^{1986}\right)⋮14\)
NA
3
19 tháng 1 2016
a,1-3+5-7+9-.......+33-35
=(1+5+9+....+33)-(3+7+11+...+35)
=153-171
=-18
Tick mk vài cái lên 300 mk giải nốt phần b
27 tháng 3 2015
A= \(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{35}+\frac{1}{99}=\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}\)
\(2A=\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.6}+...+\frac{2}{9.11}\)
\(2A=1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{9}-\frac{1}{11}\)
\(2A=1-\frac{1}{11}=\frac{10}{11}\)
\(A=\frac{10}{11}:2=\frac{5}{11}\)
27 tháng 3 2015
\(D=\frac{3^2}{1.4}+\frac{3^2}{4.7}+...+\frac{3^2}{13.16}\)
\(D=3.\left(\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{13.16}\right)\)
\(D=3.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{13}-\frac{1}{16}\right)\)
\(D=3.\left(1-\frac{1}{16}\right)=3.\frac{15}{16}=2\frac{13}{16}\)
KV
12 tháng 10 2023
a) (3⁵ . 3⁷) : 3¹⁰ + 5 . 2⁴ - 7³ : 7
= 3¹² : 3¹⁰ + 5.16 - 7²
= 3² + 80 - 49
= 9 + 31
= 40
b) (7⁵ + 7⁹) . (5⁴ + 5⁶) . (3³.3 - 9²)
= (7⁵ + 7⁹) . (5⁴ + 5⁶) . (81 - 81)
= (7⁵ + 7⁹) . (5⁴ + 5⁶) . 0
= 0
vào câu hỏi tt ý bn! có đầy ra
B=3+33+35+....+31991
3B=33+35+....+31991+31993
3B-B=(33+35+....+31991+31993)-(3+33+35+....+31991)
B= (31993-3):2
Chúc bạn học tốt !