\(T=3+8+15+24+35+...+9800+9999\) (sửa 3+5 thành 3+8)
Ta thấy :
\(3=2^2-1\)
\(8=3^2-1\)
\(15=4^2-1\)
\(24=5^2-1\)
\(.....\)
\(9800=99^2-1\)
\(9999=100^2-1\)
\(\Rightarrow T=1^2+2^2+3^2+...+100^2+\left(-1\right).100\)
\(\Rightarrow T=\dfrac{100.\left(100+1\right)\left(2.100+1\right)}{6}-100\)
\(\Rightarrow T=\dfrac{100.101.201}{6}-100=338350-100=338250\)
Tích sau có tận cùng bao nhiêu chữ số 0? 3 × 8 × 15 × 24 × 35 × … × 9603 × 9800
Tính nhanh 15/16 × 24/25 × 35/36 ×...× 9999/10000
4/3* 9/8*16/15*25/24*.....*9801/9800
B=(1+1/15)*(1+1/24)*(1+1/35)*...*(1+1/9999)
tính nhanh: \(1\frac{1}{4}\times1\frac{1}{8}\times1\frac{1}{15}\times1\frac{1}{24}\times1\frac{1}{35}\times...\times1\frac{1}{9800}\)
a=1/5+1/15+1/35..........+1/9999
a=1/5+1/15+1/35+.........+1/9999
1/3+1/15+1/35+...+1/9999
Tính nhanh:
A = [1 + 1/5] * [1 + 1/24] * [1 + 1/35] * ... * [1 + 1/9999]
