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If a ,a1, a2, a3, a(2n),b are in A.P. a...

If `a ,a_1, a_2, a_3, a_(2n),b` are in A.P. and `a ,g_1,g_2,g_3, ,g_(2n),b` . are in G.P. and `h` s the H.M. of `aa n db ,` then prove that `(a_1+a_(2n))/(g_1g_(2n))+(a_2+a_(2n-1))/(g_1g_(2n-1))++(a_n+a_(n+1))/(g_ng_(n+1))=(2n)/h`

Text Solution

Verified by Experts

Here,
`a+b=a_(1)+a_(2n)=a_(2)+a_(2n-1)=….=a_(n)+a_(n+1)`
`ab=g_(1)xxg_(2n)=g_(2)xxg_(2n-1)=…=g_(n)xxg_(n+1)`
`rArrandh=(2ab)/(a+b)`
`therefore` Sum of given series=`(n(a+b))/(ab)=(2n)/h`
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