A=1/3+1/32+...+1/3100
=>1/3A=1/32+1/33+..+1/3101
=>1/3A-A=1/3101-1/3
-2/3A=1/3101-1/3
A=(1/3101-1/3).(-3/2)=-1/2.3100+1/2
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Các câu hỏi tương tự
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}
Đọc tiếp
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 \(\dfrac{-1}{2}\)
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 .....
tinh S= 1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+...+100)
Chứng minh rằng :100- ( 1+1/2+1/3+...+1/100)=1/2+2/3+3/4+...+99/100
tinh1/2(1+2)+1/3(1+2+3)+....+1/100(1+2+3+...+100)
Tính tổng:
S = 1 + 1/2 . (1 + 2) + 1/3 . (1 + 2 + 3) + 1/4 . (1 + 2 + 3 + 4) + ... + 1/100 . (1 + 2 + 3 + ... + 99 + 100).
Tinh
A=1+1/2(1+2)+1/3(1+2+3)+...+1/100(1+2+3+...+100)
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
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
Bài 1 :Rút gọn A=2^100-2^99+2^97+...+2^2 -2
B=3^100-3^99+3^98-3^97+...+3^@ +1
bài 2:
Cho C =1/3+1/3^2+1/3^3+...=1/3^99
CMR C<1/2