Đặt A=1^2-2^2+......-2016^2+2017^2
-A=2^2-1^2+........+2016^2-2015^2
ÁP dụng A^2-B^2=(A+B)(A-B)
sau đó bạn sẽ tính được A
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tinh
1+20162+20162/20172
So sánh Q=\(\frac{1-\sqrt{2}+\sqrt{3}}{1+\sqrt{2}+\sqrt{3}}+\frac{1-\sqrt{3}+\sqrt{4}}{1+\sqrt{3}+\sqrt{4}}+...+\frac{1-\sqrt{2016}+\sqrt{2017}}{1+\sqrt{2016}+\sqrt{2017}}\)với R=\(\sqrt{2017}-1\)
Tinh ket qua dung cac phep tinh sau:
a) A= \(^{2015^3-2016^3+2017^3-2018^3+2019^3^{ }-2020^3+2008^3......+2214^3-2215^3}\)
b) B= \(\frac{3^2-1}{5^2-1}.\frac{7^2-1}{9^2-1}....\frac{2011^2-1}{2013^2-1}\)
Tính P=\(\frac{1}{2\sqrt{1}+1\sqrt{2}}\)+\(\frac{1}{3\sqrt{2}+2\sqrt{3}}+...+\frac{1}{2017\sqrt{2016}+2016\sqrt{2017}}\)
Giải pt
1)x+y+z+8=\(2\sqrt{x-1}\)+\(4\sqrt{y-2}\)+\(6\sqrt{z-3}\)
2)\(\sqrt{x}+\sqrt{x+1}=1\)
3)\(\left(1+\sqrt{x^2+2017+2016}\right)\)\(\left(\sqrt{2016+x}-\sqrt{x+1}\right)\)=2015
\(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...+\sqrt{1+\frac{1}{2016^2}+\frac{1}{2017^2}}\)
tính tổng
CMR:
\(A=\sqrt{\dfrac{1}{1^2}+\dfrac{1}{2^2}+\dfrac{1}{3^2}}+\sqrt{\dfrac{1}{1^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}}+\sqrt{\dfrac{1}{1^2}+\dfrac{1}{2016^2}+\dfrac{1}{2017^2}}+\sqrt{\dfrac{1}{1^2}+\dfrac{1}{2017^2}+\dfrac{1}{2018^2}}\)là 1 số hữu tỉ
Tính P = \(\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+\sqrt{1+\frac{1}{4^2}+\frac{1}{5^2}}+...+\sqrt{1+\frac{1}{2016^2}+\frac{1}{2017^2}}\)
Chứng minh :
\(\frac{1}{2}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+....+\frac{1}{2017\sqrt{2016}}< 2\)< 2