Ta có công thức 1+2^3+3^3+...+n^3= (n(n+1)/2)^2
=>1+2^3+3^3+...+100^3= (100(100+1)/2)^2=25502500
Ta có công thức 1+2^3+3^3+...+n^3= (n(n+1)/2)^2
=>1+2^3+3^3+...+100^3= (100(100+1)/2)^2=25502500
Chứng minh rằng 1/3 + 2/3^2 + 3/3^3 + .....+ 100/3^100 < 3/4?
CMR : 1/3 - 2/3^2 + 3^3 - 4/3^4 + .... + 99/3^99 - 100/3^100 < 3/16
tính :1*2-1/2!-3*2-1/3!+3*4-1/4!+...+99*100-1/100!
cho bieu thuc a=-1/3+1/3^2-1/3^3+1/3^4-1/3^5+...+1/3^100 tinh gia tri cua bieu thuc b=4/a/+1/3^100
CMR: \(C=\dfrac{1}{3}+\dfrac{2}{3^2}+\dfrac{3}{3^3}+...+\dfrac{99}{3^{99}}+\dfrac{100}{3^{100}}< \dfrac{3}{4}\)
Cho biểu thức \(C=\dfrac{1}{3}-\dfrac{2}{3^2}+\dfrac{3}{3^3}-\dfrac{4}{3^4}+...+\dfrac{99}{3^{99}}-\dfrac{100}{3^{100}}\)
Chứng minh \(C< \dfrac{3}{16}\)
N=1/2^3 +1/3^3 + 1/4^3+...+1/100^3
Chứng minh: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...................+\frac{100}{3^{100}}< \frac{3}{4}\)
Chứng minh: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...................+\frac{100}{3^{100}}< \frac{3}{4}\)
Chứng minh rằng: \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+....................+\frac{100}{3^{100}}< \frac{3}{4}\)