Question

Qual é o valor da soma 1 + 2 + 3 + 4 + 5 + ⋯ + 96 + 97 + 98 + 99 + 100?

Answer 1

$\large\boxed{\begin{array}{l} \rm \: 1 + 2 + 3 + 4 + 5 + ... + 96 + 97 + 98 + 99 + 100 \\ \\ \rm \: S_n = \dfrac{(a_1 + a_n) \: . \: n}{2} \rightarrow \begin{cases} \rm \: a_1 = 1 \\ \rm \: a_n = 100 \\ \rm \: n = 100\end{cases} \\ \\ \rm \: S _{100} = \dfrac{( a _1 + a_{100}) \: .100}{2} \\ \\ \rm \: S _{100} = \dfrac{(1 + 100) \: . \: 100}{2} \\ \\ \rm \: S _{100} = \dfrac{101 \: . \: 100}{2} \\ \\ \rm \:S _{100} = \dfrac{10100}{2} \\ \\ \boxed{ \boxed{ \boxed{ \rm{S _{100} = 5 050}}}}\end{array}}$

Answer 2

$\sf S_n=\dfrac{(a_1+a_n)\cdot n}{2}$

$\sf S_{100}=\dfrac{(1+100)\cdot100}{2}$

$\sf S_{100}=\dfrac{101\cdot100}{2}$

$\sf S_{100}=\dfrac{10100}{2}$

$\boxed{\boxed{\sf S_{100}=5050}}$