Question

Hallar H+F:
H= 1+2+3+4+....+20
F=1+2+3+4+....+26

Answer 1

Dentro de la sumatorias existen varias que son muy usadas, una de ellas es:

                            $\boxed{\boldsymbol{\vphantom{\Bigg|}\hphantom{a}\sf{1+2+3+\cdots+n =\dfrac{n(n+1)}{2}}\hphantom{a}}}$

Entonces

       $\begin{array}{ccccccccccccccc}\begin{array}{c}\bf{Calculemos\ H}\\\\\sf{H=1+2+3+4+\cdots + 20}\\\\\sf{H=\dfrac{20(20 + 1)}{2}}\\\\\sf{H=\dfrac{\not\!20(21)}{\not\!2}}\\\\\sf{H=10(21)}\\\\\boxed{\boldsymbol{\sf{H=210}}}\end{array}&&&&\begin{array}{c}\bf{Calculemos\ F}\\\\\sf{F=1+2+3+4+\cdots + 26}\\\\\sf{F=\dfrac{26(26 + 1)}{2}}\\\\\sf{F=\dfrac{\not\!26(27)}{\not\!2}}\\\\\sf{F=13(27)}\\\\\boxed{\boldsymbol{\sf{F=351}}}\end{array}\end{array}$

Nos piden

                                               $\begin{array}{c}\sf{H + F = 210 + 351}\\\\\boxed{\boxed{\boldsymbol{\red{\sf{H + F = 561}}}}}\end{array}$

                                            $\boxed{\sf{{R}}\quad\raisebox{10pt}{ \sf{\red{O}} }\!\!\!\!\raisebox{-10pt}{ \sf{\red{O}} }\quad\raisebox{15pt}{ \sf{{G}} }\!\!\!\!\raisebox{-15pt}{ \sf{{G}} }\quad\raisebox{15pt}{ \sf{\red{H}} }\!\!\!\!\raisebox{-15pt}{ \sf{\red{H}} }\quad\raisebox{10pt}{ \sf{{E}} }\!\!\!\!\raisebox{-10pt}{ \sf{{E}} }\quad\sf{\red{R}}}\hspace{-64.5pt}\rule{10pt}{.2ex}\:\rule{3pt}{1ex}\rule{3pt}{1.5ex}\rule{3pt}{2ex}\rule{3pt}{1.5ex}\rule{3pt}{1ex}\:\rule{10pt}{.2ex}$