Đặt \(A=\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\cdots+\frac{1}{44\cdot49}\)

\(=\frac15\left(\frac{5}{4\cdot9}+\frac{5}{9\cdot14}+\cdots+\frac{5}{44\cdot49}\right)\)

\(=\frac15\left(\frac14-\frac19+\frac19-\frac{1}{14}+\frac{1}{14}-\frac{1}{19}+\cdots+\frac{1}{44}-\frac{1}{49}\right)\)

\(=\frac15\left(\frac14-\frac{1}{49}\right)=\frac15\cdot\frac{45}{196}=\frac{9}{196}\)

Đặt B=3+5+7+...+49

Số số hạng của dãy số là: \(\frac{49-3}{2}+1=\frac{46}{2}+1=24\) (số)

Tổng của dãy số là \(\left(49+3\right)\cdot\frac{24}{2}=52\cdot\frac{24}{2}=26\cdot24=624\)

\(M=\left(\frac{1}{4\cdot9}+\frac{1}{9\cdot14}+\cdots+\frac{1}{44\cdot49}\right)\cdot\frac{1-3-5-\cdots-49}{89}\)

\(=\frac{9}{196}\cdot\frac{1-624}{89}=\frac{9}{196}\cdot\frac{-623}{89}=\frac{9}{196}\cdot\left(-7\right)=-\frac{9}{28}\)

Đặt tổng A ta có :

\(A=\frac{1}{2}+\frac{1}{4}+\frac{1}{35}+...+\frac{1}{4850}\)

\(\frac{3}{2}A=\frac{3}{4}+\frac{3}{28}+\frac{3}{70}+\frac{1}{130}+...+\frac{3}{9700}\)

\(\frac{3}{2}A=\frac{3}{1.4}+\frac{3}{4.7}+...+\frac{3}{97.100}\)

\(\frac{3}{2}A=1-\frac{1}{100}=\frac{99}{100}\)

\(\Rightarrow A=\frac{33}{50}\)

Ta có :

\(\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}\)

\(=\frac{1}{1.2}+\frac{1}{2.7}+\frac{1}{7.5}+\frac{1}{5.13}+\frac{1}{13.8}+\frac{1}{8.19}\)

Giá trị không đổi khi cả tử và mẫu cùng nhân với 2, ta được :

\(\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}+\frac{2}{16.19}\)

\(=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+...+\frac{1}{16}-\frac{1}{19}\right)\)

\(=\frac{2}{3}.\left(1-\frac{1}{19}\right)=\frac{2}{3}.\frac{18}{19}=\frac{12}{19}\)

\(A=\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}=\frac{1}{2}.\left(\frac{1}{4}+\frac{1}{28}+\frac{1}{70}+\frac{1}{130}+\frac{1}{208}+\frac{1}{304}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1.4}+\frac{1}{4.7}+\frac{1}{7.10}+\frac{1}{10.13}+\frac{1}{13.16}+\frac{1}{16.19}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}\right)\)

\(=\frac{1}{2}.\left(\frac{1}{1}-\frac{1}{19}\right)=\frac{9}{19}\)

đề kiu tính hợp lý hay tính bình thường

12/19

N = 2/4+2/28+2/70+2/130+2/208+2/304

N = 2/1.4+2/4.7+2/7.10+2.......

c1: Quy đồng mẫu rồi cộng tử

c1:Phân tích mẫu rồi triệt tiêu

Bằng 12/19

k nhé

khó quá

\(C=\frac{1}{2}+\frac{1}{14}+\frac{1}{35}+\frac{1}{65}+\frac{1}{104}+\frac{1}{152}\)

\(C=\frac{1}{1.2}+\frac{1}{2.7}+\frac{1}{7.5}+\frac{1}{5.13}+\frac{1}{13.8}+\frac{1}{8.19}\)

\(C=\frac{2}{1.4}+\frac{2}{4.7}+\frac{2}{7.10}+\frac{2}{10.13}+\frac{2}{13.16}+\frac{2}{16.19}\)

\(C=\frac{2}{3}.\left(\frac{3}{1.4}+\frac{3}{4.7}+\frac{3}{7.10}+\frac{3}{10.13}+\frac{3}{13.16}+\frac{3}{16.19}\right)\)

\(C=\frac{2}{3}.\left(\frac{1}{1}-\frac{1}{4}+\frac{1}{4}-\frac{1}{7}+\frac{1}{7}-\frac{1}{10}+\frac{1}{10}-\frac{1}{13}+\frac{1}{13}-\frac{1}{16}+\frac{1}{16}-\frac{1}{19}\right)\)

\(C=\frac{2}{3}.\left(1-\frac{1}{19}\right)\)

\(C=\frac{2}{3}.\frac{18}{19}=\frac{12}{19}\)

C= 1/2 +1/14 +1/35 +1/65 +1/104+1/152 =12/19

\(\frac{12}{19}\)

M=1/2+1/2.7+1/7.5+1/5.13+1/13.8+1/8.19

M=1/2-1/2+1/7-1/7+1/5-1/5+1/13-1/13+1/8-1/8+1/19

M=1/2-1/19

M=17/38