12 + 22 + 32 + ... + 1002
= 1 + 2.(1 + 1) + 3.(2 + 1) + ... + 100.(99 + 1)
= 1 + 1.2 + 2 + 2.3 + 3 + .... + 99.100 + 100
= (1.2 + 2.3 + .... + 99.100) + (1 + 2 + 3 + ... + 100)
= \(\frac{99.100.101}{3}+\frac{100.101}{2}\)
= 333300 + 5050
= 338350
1/2+2/2^2+3/2^3+4/2^4+...+100/2^100
cm 1/2+2/2^2+3/2^3+4/2^4+...+100/2^100<2
c/m
a/
1/2!+2/3!+3/4!+...+99/100!<1
b/
1*2-1/2!+2*3-1/3!+3*4-1/4!+...+99*100-1/100!<2
1.Tính
B=1/2+2/2^2+3/2^3+4/2^4+.....+99/2^99+100/2^100
1/ Cho A= \(\dfrac{1}{3}\)-\(\dfrac{2}{3^2}\)+\(\dfrac{3}{3^3}\)-\(\dfrac{4}{3^4}\)+.....+\(\dfrac{99}{3^{99}}\)-\(\dfrac{100}{3^{100}}\) Chứng minh A < \(\dfrac{3}{16}\)
2/ Cho B=(\(\dfrac{1}{2^2}\)-1)(\(\dfrac{1}{3^2}\)-1)....(\(\dfrac{1}{100^2}\)-1) So sánh B và \(\dfrac{-1}{2}\)
Chứng minh rằng:
a) A=1/3+1/(3^2)+1/(3^3)+...+1/(3^99)<1/2
b) B=3/(1^2*2^2)+5/(2^2*3^2)+7/(3^2*4^2)+...+19/(9^2*10^2)<1
c) C=1/3+2/(3^2)+3/(3^3)+4/(3^4)+...+100/(3^100)<3/4
Tính:
B = 1/2 + 2/2^2 + 3/2^3 + 4/2^4 + .......... + 100/2^100
Cho M=1/2+2/2^2+3/2^3+4/2^4+...+102/2^100 Tính N=M+102/2^100
1+ 1/2(1+2) + 1/3(1+2+3) +1/4(1+2+3+4) +....+1/100(1+2+3+..+100)
Ai giúp mk vs .....
chứng tỏ rằng
C = \(\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}< \frac{1}{3}\)
D = \(\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\frac{4}{3^4}+...+\frac{100}{3^{100}}< \frac{3}{4}\)
