Ta có : 1/2^2<1/1.2
1/3^2 < 1/2.3
1/4^2<1/3.4
................
.............
1/50^2<1/49.50
=> 1/2^2+1/3^2+1/4^2+1/5^2+.....+1/50^2 < 1/1.2+1/2.3+1/3.4+....+1/49.50
=> 1/2^2+1/3^2+1/4^2+1/5^2+.....+1/50^2 < 1-1/50
=> 1/2^2+1/3^2+1/4^2+1/5^2+.....+1/50^2 < 49/50 < 1
Vậy 1/2^2+1/3^2+1/4^2+1/5^2+.....+1/50^2 < 1
E=-1/3.(1+2+3)-1/4.(1+2+3+4)-...-1/50.(1+2+3+4+...+50)
E=-1/3.(1+2+3)-1/4.(1+2+3+4)-...-1/50.(1+2+3+4+...+50)
Giúp mình với
Tính tổng :\(S=1+\frac{1}{2}.\left(1+2\right)+\frac{1}{3}.\left(1+2+3\right)+\frac{1}{4}.\left(1+2+3+4\right)+....+\frac{1}{50}.\left(1+2+3+4+....+50\right)\)
50-(1+1/3+........+1/50)=1/2+2/3+3/4+.......+49/50
Chứng minh rằng:
a) 1/2^2 + 1/3^2 + 1/4^2 + ... + 1/n^2 < 1
b) 1/26 + 1/27 + 1/28 + ... + 1/50 = 1 – 1/2 + 1/3 – 1/4 + ... + 1/49 – 1/50
1) So sánh :
Tổng 3 + 1/2^2 + 1/3^2 + 1/4^2 + ......... + 1/50^2 với 4
A=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2
A=1/1^2+1/2^2+1/3^2+1/4^2+...+1/50^2
tính : 1/1+2+1/1+2+3+1/1+2+3+4+........+1/1+2+3+...+50
tinh (1/2^2-1)(1/3^2-1)(1/4^2-1)....(1/50^2-1)
