5/3+8/3^2 + 11/3^3+…+ 302/3^100
1^3+2^3+3^3+...+100^3/1×5+2×8+3×11+...+100×302 rút gọn ps
chứng minh: 23/19 < 5/3 + 8/32 + 11/33 + ...+ 302/3100 < 7/2
mink đg cần gấp mai phải nộp bài rùi !!!
Cho G=\(\frac{5}{3}+\frac{8}{3^2}+\frac{11}{3^3}+...+\frac{302}{3^{100}}\)
Chứng minh rằng 11/3<G<7/2
C=(5/3)+(8/3^2)+(11/3^3)+...+(302/3^100)
CMR: (2 và 5/9)<C<(3 và 1/2)
Làm cho mình nhanh nha
Cho G=5/3+8/3^2+11/3^3+...+302/3^100.Chứng minh 2 5/9<G<3 1phần 2
3G = 3(5/3+8/3^2+11/3^3+...+302/3^100) = 5 + 8/3 + 11/3^2 + ... + 302/3^99
3G - G = ( 5 + 8/3 + 11/3^2 + ... + 302/3^99 ) - ( 5/3+8/3^2+11/3^3+...+302/3^100 )
2G = 5 + 8/3 + 11/3^2 + ... + 302/3^99 - 5/3 - 8/3^2 - 11/3^3 - ... - 302/3^100
2G = 5 + 1 + 1/3 + 1/3^2 + ... + 1/3^98 - 302/3^100 (1)
Đặt B = 1/3 + 1/3^2 + 1/3^3 + ... + 1/3^98
3B = 1 + 1/3 + 1/3^2 + ... + 1/3^97
3B - B = 1 + 1/3 + 1/3^2 + ... + 1/3^97 - 1/3 - 1/3^2 - 1/3^3 - ... - 1/3^98
2B = 1 - 1/3^98
B = 1/2 - 1/3^98 (2)
Từ (1) và (2) => 2G = 5 + 1 + 1/3 + 1/3^2 + ... + 1/3^98 - 302/3^100 = 6 + 1/2 - 1/3^98
=> G = 3 + 1/4 - 1/3^98
ta có 0 < 1/4 - 1/3^98 < 1/2
=> 3 < 3 + 1/4 - 1/3^98 < 3 + 1/2
suy ra 2 + 5/9 < G < 3 + 1/2
Cho G= \(\frac{5}{3}+\frac{8}{3^2}+\frac{11}{3^3}+\frac{302}{3^{100}}\)
CMR \(2\frac{5}{9}< G< 3\frac{1}{2}\)
S=1+2-3-4+5+6-7-8+9+10-11-12+13+14...-299-100+301+302
Cho G = 5/3 + 8/32 + 11/33 + ........ + 302/3100 . Chứng minh rằng 2 5/9 ( hỗn số) < G < 3 1/2 ( hỗn số )
tính
a=100+98+96+.....+2-97-95-93-.....-1
b=1+2-3-3=5+6-7-8+9+10-11-12+.......-299-300+301+302
Ta có:
A = 100 + 98 + 96 + .........+ 2 - 97 - 95 - 93 -...- 1
<=> 100 + 98 + 96 + ... + 2 - (97+ 95 + 93 + ... + 1)
<=> 50 x (100 + 2) : 2 - 33 x (97+1) : 2
<=> 2550 - 1617
<=> 933