A =\(\frac{5}{11x16}+\frac{5}{16x21}+\frac{5}{21x26}+.......+\frac{5}{61x66}\) Tính Nhanh Tổng Sau
Tích Sau Có Tận cùng là bao nhiêu chữ số 0 ? :1 x 2 x 3 x ........ x 99 x 100 ?
Ai đúng Mình Tích Cho
Và Mình LÀ Con TRAI
\(A=\frac{5}{11x16}+\frac{5}{16x21}+\frac{5}{21x26}+....+\frac{5}{61x66}\)
\(C=\frac{2}{3x4}+\frac{2}{4x5}+....+\frac{2}{40x41}+\frac{2}{41x42}\)
Ai nhanh mk tik nha!!!
Ta có : \(C=\frac{2}{3.4}+\frac{2}{4.5}+\frac{2}{5.6}+......+\frac{2}{41.42}\)
\(C=2\left(\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+.....+\frac{1}{41.42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+.....+\frac{1}{41}-\frac{1}{42}\right)\)
\(C=2\left(\frac{1}{3}-\frac{1}{42}\right)\)
\(C=2.\frac{13}{42}=\frac{13}{21}\)
Các bạn chỉ cần trả lời câu C thôi nha!!!
Ta có : \(A=\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+......+\frac{5}{61.66}\)
\(\Rightarrow A=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{61}-\frac{1}{66}\)
\(\Rightarrow A=\frac{1}{11}-\frac{1}{66}\)
\(\Rightarrow A=\frac{5}{66}\)
Tính nhanh
\(\frac{5}{11x16}+\frac{5}{16x21}+.........+\frac{5}{61x66}\)
\(\frac{5}{11x16}+\frac{5}{16x21}+...+\frac{5}{61x66}\)
\(=\frac{5}{11}-\frac{5}{16}+\frac{5}{16}-\frac{5}{21}+...+\frac{5}{61}-\frac{5}{66}\)
\(=\frac{5}{11}-\frac{5}{66}+0+...+0\)
\(=\frac{25}{66}\)
~ Ủng hộ nhé anh chị em ~
\(=\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\)
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{21}\)
\(=\frac{1}{11}-\frac{1}{21}\)
\(=\frac{21}{231}-\frac{11}{231}\)
\(=\frac{10}{231}\)
sorry 4 dòng cuối ghi lộn
\(=\frac{1}{11}+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)-\frac{1}{66}\)
\(=\frac{1}{11}-\frac{1}{66}\)
\(=\frac{6}{66}-\frac{1}{66}\)
\(=\frac{5}{66}\)
Tính nhanh
\(C=\frac{1}{11X16}+\frac{1}{16x21}+\frac{1}{21x26}+...\frac{1}{56x61}+\frac{1}{61x66}\)
\(C=\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}=\frac{5}{5}\cdot\left(\frac{1}{11\cdot16}+\frac{1}{16\cdot21}+...+\frac{1}{61\cdot66}\right)\)
\(=\frac{1}{5}\cdot\left(\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+...+\frac{5}{61\cdot66}\right)=\frac{1}{5}\cdot\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(=\frac{1}{5}\cdot\left[\left(\frac{1}{11}-\frac{1}{66}\right)+\left(\frac{1}{16}-\frac{1}{16}\right)+...+\left(\frac{1}{61}-\frac{1}{61}\right)\right]\)
\(=\frac{1}{5}\cdot\left[\left(\frac{6}{66}-\frac{1}{66}\right)+0+...+0\right]=\frac{1}{5}\cdot\frac{5}{66}=\frac{1\cdot5}{5\cdot66}=\frac{1\cdot1}{1\cdot66}=\frac{1}{66}\)
Vậy \(C=\frac{1}{66}\)
Chúc bạn học tốt!^_^
Bài 2 :
E = \(\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)
E=\(\frac{1}{5}\).(\(\frac{1}{11}-\frac{1}{16}\)+\(\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+....+\frac{1}{61}-\frac{1}{66}\))
E=\(\frac{1}{5}.\left(\frac{1}{11}-\frac{1}{66}\right)\)=\(\frac{1}{5}.\frac{5}{66}=\frac{1}{66}\)
\(E=\frac{1}{11x16}+\frac{1}{16x21}+\frac{1}{21x26}+...+\frac{1}{61x66}\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}+\frac{1}{26}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}\left(\frac{1}{11}-\frac{1}{66}\right)\)
\(E=\frac{1}{5}.\frac{5}{66}\)
\(E=\frac{1}{66}\)
\(S=\frac{5^2}{1x6}+\frac{5^2}{6x11}+\frac{5^2}{11x16}+\frac{5^2}{16x21}+\frac{5^2}{21x26}\)
\(S=\frac{5^2}{1\cdot6}+\frac{5^2}{6\cdot11}+\frac{5^2}{11\cdot16}+\frac{5^2}{16\cdot21}+\frac{5^2}{21\cdot26}\)
\(S=\frac{25}{1\cdot6}+\frac{25}{6\cdot11}+\frac{25}{11\cdot16}+\frac{25}{16\cdot21}+\frac{25}{21\cdot26}\)
\(S=5\left[\frac{5}{1\cdot6}+\frac{5}{6\cdot11}+\frac{5}{11\cdot16}+\frac{5}{16\cdot21}+\frac{5}{21\cdot26}\right]\)
\(S=5\left[1-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+...+\frac{1}{21}-\frac{1}{26}\right]\)
\(S=5\left[1-\frac{1}{26}\right]=5\cdot\frac{25}{26}=\frac{125}{26}\)
Bài làm
S = \(\frac{5^2}{1.6}\)+ \(\frac{5^2}{6.11}\)+ \(\frac{5^2}{11.16}\)+ \(\frac{5^2}{16.21}\)+\(\frac{5^2}{21.26}\)
S : 5 = \(\frac{5}{1.6}\)+ \(\frac{5}{6.11}\)+ \(\frac{5}{11.16}\) + \(\frac{5}{16.21}\) + \(\frac{5}{21.26}\)
S : 5 = 1 - \(\frac{1}{6}\)+ \(\frac{1}{6}\)- \(\frac{1}{11}\) + \(\frac{1}{11}\)- \(\frac{1}{16}\)+ \(\frac{1}{16}\)- \(\frac{1}{21}\)+ \(\frac{1}{21}\)- \(\frac{1}{26}\)
S : 5 = 1 - \(\frac{1}{26}\)
S : 5 = \(\frac{25}{26}\)
S = \(\frac{125}{26}\)
\(S=\frac{5^2}{1.6}+\frac{5^2}{6.11}+\frac{5^2}{11.16}+\frac{5^2}{16.21}+\frac{5^2}{21.26}\)
\(S=5.\left(\frac{5}{1.6}+\frac{5}{6.11}+\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}\right)\)
\(S=5\left(\frac{1}{1}-\frac{1}{6}+\frac{1}{6}-\frac{1}{11}+\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}\right)\)
\(S=5\left(1-\frac{1}{26}\right)\)
\(S=5.\frac{25}{26}\)
=>\(S=\frac{125}{26}\)
Tính \(A=\frac{55}{11X16}+\frac{55}{16X21}+\frac{55}{21X26}+\frac{55}{26X31}+\frac{55}{31X36}+\frac{55}{36X41}\)
\(\frac{55}{16.21}\)chứ nhỉ.
A=\(\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+\frac{55}{26.31}+\frac{55}{31.36}+\frac{55}{36.41}\)
A= 11.\(\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+....+\frac{1}{36}-\frac{1}{41}\right)\)
A= 11\(\left(\frac{1}{11}-\frac{1}{41}\right)\)
A= 11.\(\frac{30}{451}\)
A= \(\frac{30}{41}\)
\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+....+\frac{55}{36.41}\)
\(=11.\left(\frac{5}{11.16}+\frac{5}{16.21}+\frac{5}{21.26}+.....+\frac{5}{36.41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+....+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=1-\frac{11}{41}\)
\(=\frac{30}{41}\)
\(A=\frac{55}{11X16}+\frac{55}{16X21}+\frac{55}{21X26}+\frac{55}{26X31}+\frac{55}{31X36}+\frac{55}{36X41}\)
\(A=\frac{55}{11.16}+\frac{55}{16.21}+\frac{55}{21.26}+......+\frac{55}{36.41}\)
\(=11\left(\frac{5}{11.16}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.......+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11.\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
toán 5 | Diễn đàn HOCMAI - Cộng đồng học tập lớn nhất Việt Nam
\(A=\frac{55}{11X16}+\frac{55}{16X21}+\frac{55}{21X26}+\frac{55}{26X31}+\frac{55}{31X36}+\frac{55}{36X41}\)
\(A=11X\left(\frac{5}{11X16}+\frac{5}{16X21}+\frac{5}{21X26}+\frac{5}{26X31}+\frac{5}{31X36}+\frac{5}{36X41}\right)\)
\(A=11X\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+\frac{1}{21}-\frac{1}{26}+\frac{1}{26}-\frac{1}{31}+\frac{1}{31}-\frac{1}{36}+\frac{1}{36}-\frac{1}{41}\right)\)
\(A=11X\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(A=11X\frac{1}{11}-11X\frac{1}{41}\)
\(A=1-\frac{11}{41}\)
\(A=\frac{30}{41}\)
Tính biểu thức A bằng cách nhanh nhất
A :\(\frac{55}{11x16}+\frac{55}{16x21}+\frac{55}{21x26}+\frac{55}{26x31}+\frac{55}{31x36}+\frac{55}{36x41}\)
\(A=11\left(\frac{5}{11.6}+\frac{5}{16.21}+......+\frac{5}{36.41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+.....+\frac{1}{36}-\frac{1}{41}\right)\)
\(=11\left(\frac{1}{11}-\frac{1}{41}\right)\)
\(=11.\frac{30}{451}=\frac{30}{41}\)
tính tổng A hợp lí biết A=10/11x16+10/16x21+10/21x26+...+10/61x66
\(A=\frac{10}{11.16}+\frac{10}{16.21}+...+\frac{10}{61.66}\)
\(A=\frac{10}{5}\left(\frac{5}{11.16}+\frac{5}{16.21}+...+\frac{5}{61.66}\right)\)
\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{16}+\frac{1}{16}-\frac{1}{21}+...+\frac{1}{61}-\frac{1}{66}\right)\)
\(A=\frac{10}{5}\left(\frac{1}{11}-\frac{1}{66}\right)=\frac{10}{5}.\frac{5}{66}=\frac{5}{33}\)
Vậy A =5/33