\(linh_1=1^2-2^2+3^2-4^2+...+99^2-100^2\)
\(linh_1=\left(1^2-2^2\right)+\left(3^2-4^2\right)+-+\left(99^2-100^2\right)\)
\(linh_1=\left(1-2\right)\left(1+2\right)+\left(3-4\right)\left(3+4\right)+-+\left(99-100\right)\left(99+100\right)\)\(linh_1=-1.3+-1.7+-.+-1.199\)
\(linh_1=\left(-3\right)+\left(-7\right)+-+\left(-199\right)\)
Đến đây dễ r
\(linh_2=1.2^2+2.3^2+3.4^2+...+98.99^2\)
\(linh_2=1.2.2+2.3.3+3.4.4+-.+98.99.99\)
\(linh_2=1.2.\left(3-1\right)+2.3.\left(4-1\right)+3.4.\left(5-1\right)+-+98.99.\left(100-1\right)\)\(linh_2=1.2.3-1.2+2.3.4-2.3+3.4.5-3.4+-+98.99.100-98.99\)\(linh_2=\left(1.2.3+2.3.4+3.4.5+-+98.99.100\right)-\left(1.2+2.3+3.4+-+98.99\right)\)\(linh_3=1.2.3+2.3.4+3.4.5+-+98.99.100\)
\(4linh_3=1.2.3.4+2.3.4.\left(5-1\right)+3.4.5.\left(6-2\right)+...+98.99.100.\left(101-97\right)\)
\(4linh_3=1.2.3.4+2.3.4.5-1.2.3.4+3.4.5.6-2.3.4.5+-+98.99.100.101-97.98.99.100\)
\(4linh_3=98.99.100.101\)
\(linh_3=\dfrac{98.99.100.101}{4}=24497550\)
\(linh_4=\)\(1.2+2.3+3.4+-.+98.99\)
\(3linh_4=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+-+98.99.\left(100-97\right)\)
\(3linh_4=1.2.3+2.3.4-1.2.3+3.4.5-2.3.4+...+98.99.100-97.98.99\)
\(3linh_4=98.99.100\)
\(linh_4=\dfrac{98.99.100}{3}=125400\)
Lấy \(linh_3-linh_4\) là ok
