Tính tổng: a) S= 1^2+2^2+3^2+...+99^2
b) S= 1.3+3.5+5.7+...+97.99
Giúp mình với !!
1/ Tính nhanh:
A = 1.3 + 3.5 + 5.7 + ... + 97.99
2/ Cho S = 2 + 22 + 23 + .......... + 299 + 2100
Chứng minh rằng : S chia hết cho 6 ; 14 ; 30 ; 31
Tính nhanh
B=3^2/1.3+3^2/3.5+3^2/5.7+...+3^2/95.97+3^2/97.99
=3.(3/1.3+3/3.5+3/5.7+...+3/95.97+3/97.99)
=3(1-1/3+1/3-1/5+1/5-1/7+...+1/95-1/97+1/97-1/99)
=3[(1-1/99)+(1/5-1/5)+(1/7-1/7)+...+(1/97-1/97)]
=3(1-1/99)=3(99/99-1/99)=3.98/99=1.98/33=98/33
Neu la 3 ma ko phai la 3^2 thi sao : Tinh gium minh nha .
Tính: 2/1.3+ 2/3.5+ 2/5.7+ ......... + 2/97.99
2/1.3 + 2/3.5 + 2/5.7 +...+ 2/97.99
=(1/1-1/3)+(1/3-1/5)+(1/5-1/7)+...+(1/97-1/99)
=1-1/99=98/99
tính tổng S=2/1.3+2/3.5+2/5.7+2/7.9+2/9.11
\(S=\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}\)
\(=\dfrac{1}{1}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}\)
\(=\dfrac{1}{1}-\dfrac{1}{11}=\dfrac{11}{11}-\dfrac{1}{11}=\dfrac{10}{11}\)
1/ A = 12- 22 + 32 - 42+...+ 992- 1002
2/ A = 1.3 + 3.5 + 5.7 +...+ 97.99 + 99.100
3/ A = 2.4 + 4.6 + 6.8 +...+ 99.100 + 100.102
Tính tổng
S=1^4/1.3+2^4/3.5+3^4/5.7+...+12^4/23.25
Bài này lớp 6 học rùi!
S = 312/25
\(\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{97.99}\right)-x=-\frac{100}{99}\)
\(\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{97.99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+....+\frac{1}{97}-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\left(1-\frac{1}{99}\right)-x=-\frac{100}{99}\)
\(\Rightarrow\frac{98}{99}-x=-\frac{100}{99}\)
\(\Rightarrow x=\frac{98}{99}-\left(-\frac{100}{99}\right)\)
\(\Rightarrow x=\frac{198}{99}=2\)
Vậy x = 2
tách\(\frac{2}{1.3}\)+\(\frac{2}{3.5}\)+\(\frac{2}{5.7}\)+......+\(\frac{2}{97.99}\)ra thành A
A=1/1-1/3+1/3-1/5+1/5-........+1/97-1/99
A=1-1/99=98/99
=>x=98/99-\(\frac{-100}{99}\)=2
k mình nha
Tính :
A = 1.2+2.3+3.4+...+99.100
B = 1.3+2.4+3.5+...+99.101
C = 1.3+3.5+5.7+...+97.99+99.101
D = 1.4+2.5+3.6+...+99.102
E = 12+22+32+...+992+1002
F = 1.99+2.98+3.97+...+98.2+99.1
Mình cần gấp lắm ! Ai làm được cho mình trước trình bày đầy đủ mình kick cho
Tính
a) A= 1.3+3.5+5.7+...+99.101
b)B= 1^2+3^2+5^2+...+99^2