a) \(1+2+3+4+-.+100\)
\(=\dfrac{\left(1+100\right).\left[\left(100-1\right):1+1\right]}{2}\)
\(=\dfrac{101.\left(99+1\right)}{2}\)
\(=\dfrac{101.100}{2}\)
\(=\dfrac{10100}{2}\)
\(=5050\)
b) \(1+3+5+-+151\)
\(=\dfrac{\left(1+151\right).\left[\left(151-1\right):2+1\right]}{2}\)
\(=\dfrac{152.\left(150:2+1\right)}{2}\)
\(=\dfrac{152.\left(75+1\right)}{2}\)
\(=\dfrac{152.76}{2}\)
\(=\dfrac{11552}{2}\)
\(=5776\)
c) \(2+5+8+-..+101\)
\(=\dfrac{\left(2+101\right).\left[\left(101-2\right):3+1\right]}{2}\)
\(=\dfrac{103.\left(99:3+1\right)}{2}\)
\(=\dfrac{103.\left(33+1\right)}{2}\)
\(=\dfrac{103.34}{2}\)
\(=\dfrac{3502}{2}\)
\(=1751\)
