a=1.2+2.3+3.4+...+98.99
b=12+22+32+...+982
=> a-b=(1.2+2.3+3.4+...+98.99)-(12+22+32+...+982)
=1.2+2.3+3.4+...+98.99-12-22-32-...-982
=(1.2-12)+(2.3-22)+...+(98.99-982)
=1(2-1)+2(3-2)+...+98(99-98)
=1.1+2.1+...+98.1
=1+2+3+...+98
=\(\dfrac{98.\left(98+1\right)}{2}\)
=\(\dfrac{98.99}{2}\)
=4851
Vậy a-b=4851
Đúng thì tick nha,
tính
E = 1.22+2.32+3.42+...+98.992
Tính \(A=\dfrac{1+\left(1+2\right)+...+\left(1+2+...+98\right)}{1.2+2.3+...+98.99}\)
Chứng minh rằng :\(\dfrac{1.98+2.97+3.96+...+96.3+97.2+98.1}{1.2+2.3+3.4+...+96.97+97.98+98.99}=\dfrac{1}{2}\)
Tính
E = 1.22+2.32+3.42+...+98.992
CMR:
\(B=\dfrac{1.98+2.97+3.96+...+96.3+97.2+98.1}{1.2+2.3+3.4+...+96.97+97.98+98+99}=\dfrac{1}{2}\)
a) Tính tổng : 1+ 2 + 3 +…. + n , 1+ 3 + 5 +…. + (2n -1)
b) Tính tổng : 1.2 + 2.3 + 3.4 + …..+ n.(n+1) 1.2.3+ 2.3.4 + 3.4.5 + ….+ n(n+1)(n+2)
Với n là số tự nhiên khác 0.
Các thánh giúp em zới ko hỉu gì hết trơn T-T
A=\(\dfrac{1}{1.2^2}+\dfrac{1}{2.3^2}+\dfrac{1}{3.4^2}+...+\dfrac{1}{49.50^2}\)
B=\(\dfrac{1}{2^2}+\dfrac{1}{3^2}+\dfrac{1}{4^2}+...+\dfrac{1}{50^2}\)
CM A<B
CMR:
a) \(\frac{1}{2!}+\frac{2}{3!}+\frac{3}{4!}+...+\frac{99}{100!}< 1\)
b) \(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+...+\frac{99.100-1}{100!}< 2\)
Chứng minh rằng: \(\frac{1.2-1}{2!}+\frac{2.3-1}{3!}+\frac{3.4-1}{4!}+..................+\frac{99.100-1}{100!}< 2\)