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dễ ẹc :
5+52+53+...+559+560
=(5+54)+(52+55)+(53+56)+...+(557+560)
=5+(1+53)+52+(1+53)+...+557+(1+53)
= 126 .(5+52+...+557) chia hết cho 126
(đ.p.c.m)
b: \(\Leftrightarrow\left(3x-1\right)^2=25\)
\(\Leftrightarrow3x-1\in\left\{5;-5\right\}\)
hay \(x\in\left\{2;-\dfrac{4}{3}\right\}\)
c: \(\Leftrightarrow\left(2x-5\right)^3=-81\)
\(\Leftrightarrow2x-5=-3\sqrt[3]{3}\)
hay \(x=\dfrac{5-\sqrt[3]{3}}{2}\)
5 / 14 + 18 / 35 + ( 5 / 4 - 5 / 4 ) : ( 5/12)^2
= 61 / 70 + 0 : ( 5 / 12)^2
= 61 / 70 + 0
= 61 / 70
B=1/5.(1+1/5+...+\(^{\frac{1}{5^{ }}99}\))
C=1/5.(1/5+\(\frac{1}{5}^3\)+...+\(\frac{1}{5}^{99}\))
\(-\frac{3}{5}.\frac{2}{7}+-\frac{3}{5}.\frac{5}{7}+2\frac{3}{5}\)
\(=-\frac{3}{5}\left(\frac{2}{7}+\frac{5}{7}\right)+2\frac{3}{5}\)
\(=-\frac{3}{5}+\frac{13}{5}\)
\(=\frac{10}{5}=2\)
Ta có:
B = \(\frac{-5}{3}+\frac{-5}{15}+\frac{-5}{35}+...+\frac{-5}{2499}.\)
= \(-5\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+...+\frac{1}{2499}\right)\)
= \(-5\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+...+\frac{1}{49.51}\right)\)
= \(-5\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{49}-\frac{1}{51}\right):2\)
= \(\frac{-5}{2}\left(1-\frac{1}{51}\right)\)
= \(\frac{-5}{2}.\frac{50}{51}\) = -6375
\(5+5=10\)
10