If a,a1,a2,a3,a2n,b are in A.P. and a,g1,g2,g3,,g2n,b . are in G.P. and h s the H.M. of aandb, then prove that g1g2na1+a2n+g1g2n−1a2+a2n−1++gngn+1an+an+1=h2n

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If {a},{a}_{{1}},{a}_{{2}},{a}_{{3}},{a}_{{{2}{n}}},{b} are in

Question

If $a, a_{1}, a_{2}, a_{3}, a_{2 n}, b$ are in A.P. and $a, g_{1}, g_{2}, g_{3},, g_{2 n}, b$ . are in G.P. and $h$ s the H.M. of $a a n d b,$ then prove that $\frac{a _{1} + a _{2 n}}{g _{1} g _{2 n}} + \frac{a _{2} + a _{2 n - 1}}{g _{1} g _{2 n - 1}} + + \frac{a _{n} + a _{n + 1}}{g _{n} g _{n + 1}} = \frac{2 n}{h}$

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a, a_{1}, a_{2}, a_{3}, a_{2 n}, b

are in A.P. and

a, g_{1}, g_{2}, g_{3},, g_{2 n}, b

. are in G.P. and

h

s the H.M. of

a a n d b,

then prove that

\frac{a _{1} + a _{2 n}}{g _{1} g _{2 n}} + \frac{a _{2} + a _{2 n - 1}}{g _{1} g _{2 n - 1}} + + \frac{a _{n} + a _{n + 1}}{g _{n} g _{n + 1}} = \frac{2 n}{h}

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Question Text

a, a_{1}, a_{2}, a_{3}, a_{2 n}, b

are in A.P. and

a, g_{1}, g_{2}, g_{3},, g_{2 n}, b

. are in G.P. and

h

s the H.M. of

a a n d b,

then prove that

\frac{a _{1} + a _{2 n}}{g _{1} g _{2 n}} + \frac{a _{2} + a _{2 n - 1}}{g _{1} g _{2 n - 1}} + + \frac{a _{n} + a _{n + 1}}{g _{n} g _{n + 1}} = \frac{2 n}{h}