Bài 2: Dãy số

nhanh lên các bạn ơi giúp mk jk

\(A=5-5^2+5^3-5^4+...-5^{98}+5^{99}\)

\(5A=5\left(5-5^2+5^3-5^4+...-5^{98}+5^{99}\right)\)

\(5A=5^2-5^3+5^4-5^5+...-5^{99}+5^{100}\)

\(5A+A=\left(5^2-5^3+...-5^{99}+5^{100}\right)+\left(5-5^2+...-5^{98}+5^{99}\right)\)

\(6A=5^{100}+5\Rightarrow A=\dfrac{5^{100}+5}{6}\)

Lời giải lớp 11

\(S=A-1=1+2^1+2^2+...+2^{20}\)

\(\left\{{}\begin{matrix}U_1=1\\q=2\end{matrix}\right.\) \(\Rightarrow S=\dfrac{u_1\left(q^{n+1}-1\right)}{q-1}=2^{21}-1\) \(\Rightarrow A=2^{21}\)

A = 4+2²+2³+2⁴+....+2²⁰

Đặt B = 2²+2³+2⁴+....+2²⁰

2B = 2³+2⁴+2⁵+....+2²¹

B = 2B - B = 2²¹ - 2²

=> A = 4 + (2²¹ - 2²)

=> A = 2²+2²¹-2²

=> A = 2²¹

5.7 + 7.9 + 9.11 + ... + 25.27 = 3245

\(B=\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2016}}\)

\(\Rightarrow\dfrac{B}{2}=\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2017}}\)

\(\Rightarrow\dfrac{B}{2}-B=\left(\dfrac{1}{2^2}+\dfrac{1}{2^3}+...+\dfrac{1}{2^{2017}}\right)-\left(\dfrac{1}{2}+\dfrac{1}{2^2}+...+\dfrac{1}{2^{2016}}\right)\)

\(\Leftrightarrow-\dfrac{B}{2}=\dfrac{1}{2^{2017}}-\dfrac{1}{2}\)

\(\Rightarrow B=1-\dfrac{1}{2^{2016}}< 1\)

đầu bài là j

a) \(100+98+96+...+2-97-95-93-...-3\)

= \(100+98+\left(96-97\right)+\left(94-95\right)+...+\left(2-3\right)\)

= \(100+98-95\) = \(103\)

b) \(2-4-6+8+10-12-14+16+...-102+104\)

= \(\left(2-4\right)+\left(-6+8\right)+\left(10-12\right)+\left(-14+16\right)+...+\left(-102+104\right)\)

= \(-2+2-2+2-2+...+2\) = \(0\)

c) \(1+2-3-4+5+6-7-8+9+10-11-12+...-111-112+113+114\)

= \(\left(1+2\right)-\left(3+4\right)+\left(5+6\right)-\left(7+8\right)+...\left(113+114\right)\)

= \(3-7+11-15+19-23+...+219-223+227\)

= \(\left(3-7\right)+\left(11-15\right)+\left(19-23\right)+...+\left(219-223\right)+227\)

= \(-4-4-4-4-...-4+227\)

= \(54\left(-4\right)+227\) = \(-216+227\) = \(11\)

\(A=-1+7-7^2+7^3-...-7^{202}\)

\(7A=7\left(-1+7-7^2+7^3-...-7^{202}\right)\)

\(7A=-7+7^2-7^3+...+7^{202}-7^{2003}\)

\(7A+A=\left(-7+...+7^{202}-7^{203}\right)+\left(-1+7-...-7^{202}\right)\)

\(8A=-7^{203}-1\Rightarrow A=\dfrac{-7^{203}-1}{8}\)

Hờ, bài toán này mà mình cứ ngồi tính tổng như thật -,-

\(\text{1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12 + ... - 111 - 112 + 113 + 114}\)\(=1+\left(2-3-4+5\right)+\left(6-7-8+9\right)+\left(10-11-12+13\right)+...+\left(110-111-112+113\right)+114\)\(=1+114=115\)

Lớp 5: chương trình nâng cao nhé các bạn! ko có số âm nhé!