Question

me ajuda nesses somatórios​

Answer 1

$x+\overset{20}{\underset{i=0}\sum}(2i-1)=\overset{20}{\underset{i=0}\sum}(2i)\\\\x+\left(\overset{20}{\underset{i=0}\sum}(2i-1)\right)-\left(\overset{20}{\underset{i=0}\sum}(2i)\right)=0\\\\x+\overset{20}{\underset{i=0}\sum}(2i-1-2i)=0\\\\x+\overset{20}{\underset{i=0}\sum}(-1)=0\\\\x+(21)(-1)=0\\\\x=21$

$\overset{15}{\underset{j=0}\sum}(1+2j)=\overset{4}{\underset{j=1}\sum}(x)+\overset{15}{\underset{j=1}\sum}(1+2j)\\\\(1+2(0))+\overset{15}{\underset{j=1}\sum}(1+2j)=\overset{4}{\underset{j=1}\sum}(x)+\overset{15}{\underset{j=1}\sum}(1+2j)\\\\(1+2(0))=\overset{4}{\underset{j=1}\sum}(x)\\\\1=4x\\\\x=\dfrac14$