Grade 12th passAlgebra
Find the value of 1/(22-1)+1/(42-1)+1/(62-1)..........1/(202-1)
Find the value of 1/(22-1)+1/(42-1)+1/(62-1)..........1/(202-1)
2 Answers
Vikas TU
Dear student
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Aditya Gupta
r th term is
ar= 1/[(2r)^2 – 1)]
= 1/[(2r – 1)(2r+1)]
so, ar= 1/2(2r – 1) – 1/2(2r+1). if we take f(r)= 1/2(2r – 1) , then obviously f(r+1)= 1/2(2r+1).
or ar= f(r) – f(r+1)
so, we want to know a1 + a2 + a3 + …......... + a10
= f(1) – f(2)
+f(2) – f(3)
+f(3) – f(4)
+........
…....
+f(9) – f(10)
+f(10) – f(11)
= f(1) – f(11)
= ½ – 1/42
= 10/21
kindly approve :)
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