Tính nhanh A = 1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+...+1/16(1+2+3+...+16)
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tính nhanh A= 1+1/2(1+2) +1/3(1+2+3)+1/4(1+2+3+4)+...+ 1/16(1+2+3+...+16)
ta có
A = \(1+\frac{1+2}{2}+\frac{1+2+3}{3}+\frac{1+2+3+4}{4}+......+\frac{1+2+3+\text{4 +....+16}}{16}\)
xét tổng S = 1+2+3+4+5+......+n = \(\frac{\left(n+1\right)n}{2}\) lấy \(\frac{S}{n}=\frac{\frac{\left(n+1\right)n}{2}}{n}=\frac{n+1}{2}\)
ta có
A=\(1+\frac{\frac{2\left(2+1\right)}{2}}{2}+\frac{\frac{3\left(3+1\right)}{2}}{3}+\frac{\frac{4\left(4+1\right)}{2}}{4}+\frac{\frac{5\left(5+1\right)}{2}}{5}+......+\frac{\frac{16\left(16+1\right)}{2}}{16}\)
A = \(1+\frac{1+2}{2}+\frac{1+3}{2}+\frac{1+4}{2}+\frac{1+5}{2}+......+\frac{1+16}{2}\)
A = \(1+\frac{1+2+1+3+1+\text{4+1+5+1+6+.....+1+16}}{2}\)
A = \(1+\frac{151}{2}\)
A = \(\frac{153}{2}\)
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Tính nhanh
A= 1+ 1/2 (1+2) +1/3 (1+2+3) +1/4 (1+2+3+4) +...+ 1/16 (1+2+3+4+...+16)
A=1+1/2x3+1/3X6+1/4X10+...+1/16X136
A=1+3/2+2+5/2+3+...+17/2
A=2/2+3/2+4/2+5/2+6/2+...+17/2
A=2+3+4+5+...+16+17/2
A=(2+17)x16:2/2
A=19x16:2/2
A=304:2/2
A=152/2
A=76
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b tính nhanh A= 1+1/2(1+2) +1/3(1+2+3)+1/4(1+2+3+4)+...+ 1/16(1+2+3+...+16)
Tính nhanh:
A = 1+ 1/2(1+2) + 1/3+(1+2+3) +1/4(1+2+3+4)+.....+1/16(1+2+3+....+16)
Tính nhanh
A=1+1/2[1+2]+1/3[1+2+3]+1/4[1+2+3+4]+...+1/16[1+2+3+...+16]
Tính Nhanh
A=1+1/2[1+2]+1/3[1+2+3]+1/4[1+2+3+4]+...+1/16[1+2+3+...+16]
Tính nhanh
a) 2.4.(3^2+1)(3^4+1)...(3^16+1)
b) 2.(3+1).(3^2+1)(3^4+1)...(3^16+1)
c) 8.(3^2+1)(3^4+1)...(3^16+1)
TUI ĐANG GẤP CHO TÔI HỎI BÀI NÀY LỚP 2 NHA\\\\
AN CÓ 180 CÁI KẸO.BÌNH CÓ 160. HỎI BÌNH CÓ MẤY CÁI KẸO
a) Ta có: \(2.4.\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(=3^{32}-1\)
b) \(2.\left(3+1\right)\left(3^2+1\right)...\left(3^{16}+1\right)\)
\(=\left(3-1\right)\left(3+1\right)\left(3^2+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^2-1\right)\left(3^2+1\right)\left(3^4+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^4-1\right)\left(3^4+1\right)\left(3^8+1\right)...\left(3^{16}+1\right)\)
\(=\left(3^8-1\right)\left(3^8+1\right)\left(3^{16}+1\right)\)
\(=\left(3^{16}-1\right)\left(3^{16}+1\right)\)
\(=3^{32}-1\)
Xem thêm câu trả lời
tính nhanh
1+1/2(1+2)+1/3(1+2+3)+1/4(1+2+3+4)+....+1/16(1+2+3+4+...+16)
Ta có :
\(1+\frac{1}{2}\left(1+2\right)+\frac{1}{3}\left(1+2+3\right)+\frac{1}{4}\left(1+2+3+4\right)+...+\frac{1}{16}\left(1+2+3+4+...+16\right)\)
\(=\)\(1+\frac{1}{2}.\frac{2\left(2+1\right)}{2}+\frac{1}{3}.\frac{3\left(3+1\right)}{2}+\frac{1}{4}.\frac{4\left(4+1\right)}{2}+...+\frac{1}{16}.\frac{16\left(16+1\right)}{2}\)
\(=\)\(1+\frac{2+1}{2}+\frac{3+1}{2}+\frac{4+1}{2}+...+\frac{16+1}{2}\)
\(=\)\(\frac{2}{2}+\frac{3}{2}+\frac{4}{2}+\frac{5}{2}+...+\frac{17}{2}\)
\(=\)\(\frac{2+3+4+5+...+17}{2}\)
\(=\)\(\frac{\frac{16\left(17+2\right)}{2}}{2}\)
\(=\)\(\frac{152}{2}\)
\(=\)\(76\)
Bài này áp dụng công thức \(1+2+3+...+n=\frac{n\left(n+1\right)}{2}\) nhé
Chúc bạn học tốt ~
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Tính nhanh: A = 1 + 1/2 . (1 + 2 ) + 1/3 . ( 1 +2+3) + ... + 1/16 ( 1+2+3+4+...+16)
Mong mọi người giúp đỡ!!!