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egorkan02
@egorkan02
July 2022
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1/(√36+√37) + 1/(√37+√38) + ... + 1/(√48+√49)
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skyne8
Verified answer
=(√36-√37)/((√36)^2 -(√37)^2) +
(√37-√38)/((√37)^2-(√38)^2)+...+
(√48-√49)/((√48)^2-(√49)^2)=
(√36-√37)/(36-37)+(√37-√38)/(37-38)
+...+(√48-√49)/(48-49)=
(√36-√37)/(-1)+(√37-√38)/(-1)+...+
(√48-√49)/(-1)=
(√36-√37+√37-√38+√38-...-√49)/(-1)=
(√36-√49)/(-1)=(6-7)/(-1)=(-1)/(-1)=1
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Verified answer
=(√36-√37)/((√36)^2 -(√37)^2) +(√37-√38)/((√37)^2-(√38)^2)+...+
(√48-√49)/((√48)^2-(√49)^2)=
(√36-√37)/(36-37)+(√37-√38)/(37-38)
+...+(√48-√49)/(48-49)=
(√36-√37)/(-1)+(√37-√38)/(-1)+...+
(√48-√49)/(-1)=
(√36-√37+√37-√38+√38-...-√49)/(-1)=
(√36-√49)/(-1)=(6-7)/(-1)=(-1)/(-1)=1