Mathematics in Ancient and Medieval India c8.s3.40

c8.s3.40

Expanding f (n+1) and f (n-1) by Taylor's Theorem, we have form (4), $1/n = U_n + 2[ f (n) + (fii(n))/(2!) + (fiv(n))/(4!) +$ $+ 1/((2p)!) f 2p(n+θ₁) - f 2p(n-θ₂) ] 7$ where 0 < θ₁ < 1, 0 < θ₂ < 1