S= 1+3+32+.......+350 (1)
=> 3S= 3+32+33+......+351 (2)
Lấy (2)-(1) ta có:
3S-S= (3+32+33+..........+351)-(1+3+32+..................+350)
2S= 351-1
S= \(\frac{3^{51}-1}{2}\)
let S be 1!(12+1+1)+2!(22+2+1)+3!(32+3+1)+...+100!(1002+100+1). Find S+1/101!.(as usual, k! = 1.2.3.....(k-1).k)
cho s=1/31+1/32+1/33+...+1/59+1/60
chung minh rang : 3/5<s<4/5
Tính tổng S=1/2+3/4+7/8+15/16+31/32+63/64+127/128-6
Cho S=\(\frac{1}{31}\)+\(\frac{1}{32}\)+\(\frac{1}{32}\)+.....+\(\frac{1}{60}\)
So sánh S với \(\frac{4}{5}\)
Cho S = \(\frac{1}{13}\)+\(\frac{1}{32}\)+ ...................+\(\frac{1}{60}\)
Chứng minh \(\frac{3}{5}\)< S < \(\frac{4}{5}\)
so sanh S=1/30+1/31+1/32+....+1/59+1/60 voi 1/2
Cho
S= \(\frac{1}{31}\)+ \(\frac{1}{32}\)+...+ \(\frac{1}{60}\)
Chúng minh rằng \(\frac{3}{5}\)< S < \(\frac{4}{5}\)
Cho S= 1/2 + 1/8 + 1/18 + 1/32 + 1/50 + 1/72 + 1/98 + 1/128 + 1/162
Chứng tỏ S < 18/19
Chứng minh rằng:
A = 1/3 + 1/32 + 1/33 + ..........+ 1/399 < 1/2
B = 3/12x 22 + 5/22 x 32 + 7/32 x 42 +............+ 19/92 x 102 < 1
C = 1/3 + 2/32 + 3/33 + 4/34 +.........+ 100/3100 ≤ 0
Tính:
S = 3/2 + 5/4 + 9/8 + 17/16 + 33/32 + 65/64 - 7