CHECK KNOWLEDGE IN A.P. G.P. H.P.
S= √(1+1/1^2+1/2^2) +√(1+1/2^2+1/3^2)+…………………………………………√(1+1/999^2+1/1000^2)
Now, S= 10k-1/1000 then find value of k(hint- √(1+1/1^2+1/2^2) are in whole square root and this use the partial fraction)if not solve this difficult problem then see the answer if still not clear then contact me
The answer is 6.
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1 solution
√(1+1/n^2+1/(n+1)^2) is nth term Can be substituted as √((n^2+n+1)^2/[n(n+1)]^2) then substituted as (n^2 +n+1)/n(n+1) Then as 1+1/n-1/n+1 Then substituting value of n from 1 to 999 Later substituted as 999+1/1-1/1000 Then later as 999+999/1000 =999999/1000 =10^6-1/1000