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" Find "F(n+1)=GMrn[(1)/(r^(2))+(1)/(2r^...

" Find "F_(n+1)=GMrn[(1)/(r^(2))+(1)/(2r^(2))+(1)/(4r^(2))+.........." up to "oo]

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Find F_("net") = GMm[ (1)/(r^(2))+ (1)/(2r^(2))+ (1)/(4r^(2))+ ...... "up to "oo] .

Find F_("net") = GMm[ (1)/(r^(2))+ (1)/(2r^(2))+ (1)/(4r^(2))+ ...... "up to "oo] .

Prove that sum_(r=0)^(n)(-1)^(r)nC_(r)[(1)/(2^(r))+(3)/(2^(2r))+(7)/(2^(3r))+(15)/(2^(4r))+...up to mterms]=(2^(mn)-1)/(2^(mn)(2^(n)-1))

Find Lt(n rarr oo) sum_(r=0)^(n-1)(1)/(sqrt(n^(2) - r^(2))

find the sum of the series sum_(r=0)^(n)(-1)^(r)*^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+(7^(r))/(2^(3r))+(15^(r))/(2^(4r))... up to m terms ]

Sigma_(r=0)^(n)(-1)^(r).^(n)C_(r)[(1)/(2^(r))+(3^(r))/(2^(2r))+...up rarr mterms ]

sum_(r=0)^n(-1)^r .^n C_r[1/(2^r)+3/(2^(2r))+7/(2^(3r))+(15)/(2^(4r))+ .....mt e r m s]= (2^(m n)-1)/(2^(m n)(2^n-1))

Lt_(n rarr oo) sum_(r=1)^(n)[(1)/(sqrt(4n^(2) - r^(2)))]