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Compute the sum
\(\frac{1}{\sqrt{100} + \sqrt{102}} + \frac{1}{\sqrt{102} + \sqrt{104}} + \frac{1}{\sqrt{104}+\sqrt{106}} + \cdots + \frac{1}{\sqrt{9998} + \sqrt{10000}}. \)Just give me a hint. Thank you!

 Apr 13, 2021
 #1
avatar+2124 
+2

Tell me if you need more help. :))

(a+b)(a-b) = a^2-b^2

 

=^._.^=

 Apr 13, 2021
 #2
avatar+2124 
+2

Also, welcome to web2.0calc :DDDD

 

=^._.^=

 Apr 13, 2021
 #3
avatar+180 
+3

TYSM, I got the answer 45. Also thanks for welcoming me. smiley

 Apr 14, 2021
 #4
avatar+2124 
+2

YAYY. :))

 

(sqrt(100)-sqrt(102)+sqrt(102)-sqrt(104)...sqrt(9998)-sqrt(10000))/-2

Everything cancels out. :DDD

(10-100)/-2=45

 

=^._.^=

catmg  Apr 14, 2021

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