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Sigma(r=0)^n (-1)^r .^nCr[1/2^r+3^r/2^(...

`Sigma_(r=0)^n (-1)^r .^nC_r[1/2^r+3^r/2^(2r)+... upto m terms]`

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sum_(r=0)^n (-1)^r .^nC_r (1+rln10)/(1+ln10^n)^r

Show that sum_(r=0)^(n) (-1)^(r ). ""^(n)C_(r ) {(1)/(2^(r )) +(3^(r ))/(2^(2r)) +(7^(r ))/(2^(3r)) +…."upto m terms"}=(2^(mn)-1)/(2^(mn)(2^(n)-1))

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))

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

sum_(r=1)^(n) (-1)^(r-1) ""^nC_r(a - r) =

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

Evaluate sum_(r=0)^n(r+1)^2*"^nC_r

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is

The sum of series Sigma_(r=0)^(r) (-1)^r(n+2r)^2 (where n is even) is