Đặt \(A=1+7^2+7^3+7^4+...+7^{99}\)

\(\Rightarrow7A=7\left(1+7^2+7^3+7^4+...+7^{99}\right)\)

\(\Rightarrow7A=7+7^3+7^4+7^5+...+7^{100}\)

\(\Rightarrow7A-A=\left(7+7^3+7^4+7^5+...+7^{100}\right)-\left(1+7^2+7^3+7^4+...+7^{99}\right)\)

\(\Rightarrow6A=7^{100}-1\)

\(\Rightarrow A=\frac{7^{100}-1}{6}\)

đặt S = 1 + 7² + 7³ + 7⁴ + .... + 7⁹⁹

=> 7S = 7 + 7³ + 7⁴ + 7⁵ + .... 7¹⁰⁰

=> 7S - S = (7 + 7³ + 7⁴ + 7⁵ + .... + 7¹⁰⁰) - (1 + 7² + 7³ + 7⁴ + .... + 7⁹⁹)

=> 6S = (7 + 7¹⁰⁰) - (1 + 7²) 

=> 6S = (7 - 1) + (7¹⁰⁰ - 7²)

=> 6S = 6 + 7¹⁰⁰ - 7²

=> S = \(\frac{6+7^{100}-7^2}{6}\)

rốt cuộc là ai đúng

\(7M=7+7^2+7^3+...+7^{101}\)

\(7M-M=\left(7+7^2+...+7^{101}\right)-\left(1+7+..+7^{100}\right)\)

\(6M=7^{101}-1\)

\(M=\frac{7^{101}-1}{6}\)

=\(\dfrac{5}{11}\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}\)

=\(\dfrac{5}{11}\times1+\dfrac{6}{11}\)

=\(\dfrac{11}{11}\)=1

\(\dfrac{5}{11}\cdot\dfrac{5}{7}+\dfrac{5}{11}\cdot\dfrac{2}{7}+\dfrac{6}{11}=\dfrac{5}{11}\cdot\left(\dfrac{5}{7}+\dfrac{2}{7}\right)+\dfrac{6}{11}=\dfrac{5}{11}\cdot1+\dfrac{6}{11}=\dfrac{5}{11}+\dfrac{6}{11}=1\)

=\(-19\frac{1}{4}\)

1.139852281

\(A=\left(4x+5\right)^2-\left(3x-7\right)^2-\left(4x-1\right)\left(4x+1\right)\)

\(=\left(4x\right)^2+2.4x.5+5^2-\left[\left(3x\right)^2-2.3x.7+7^2\right]-\left[\left(4x\right)^2-1^2\right]\)

\(=16x^2+40x+25-\left(9x^2-42x+49\right)-\left(16x^2-1\right)\)

\(=16x^2+40x+25-9x^2+42x-49-16x^2+1=-9x^2+82x-23\)

A=(4x+5)²-(3x-7)²-(4x-1)(4x+1)

=16x²+40x+25-9x²+42x-49-16x²+1

=(16x²-9x²-16x²)+(40x+42x)+(25-49+1)

=-9x²+82x-23

P=1+(-3)+5+(-7)+...17+(-19)

P=(-2)+(-2)+...+(-2)

P=(-2). 9,5 ( vì có 9,5 số -2) 

P= -19