`(1)/(2.5 )+(1)/(5.8)+(1)/(8.11)+…………+(1)/((3n-1)(3n+2))=(n)/((6n+4))`

(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+... n terms =(A)(n)/(6n+4) (B) (n)/(3n+2)(C)(n)/(4n+6)(D)(1)/(2(2n+3))

(1^(2))/(1.3)+(2^(2))/(3.5)+(3^(2))/(5.7)+.....+(n^(2))/ ((2n-1)(2n+1))=((n)(n+1))/((2(2n+1)))

Prove that (C_1)/(2) + (C_3)/(4) + (C_5)/(6) + (C_7)/(8) + …… = (2^n - 1)/(n+ 1)

(1^(4))/(1.3)+(2^(4))/(3.5)+(3^(4))/(5.7)+......+(n^(4)) /((2n-1)(2n+1))=(n(4n^(2)+6n+5))/(48)+(n)/(16(2n+1))

Prove that 5^(n) (1+(n)/(5) +(n(n-1))/(5*10) +(n(n-1)(n-2))/(5*10*15)+…oo)=3^(n) (1+(n)/(2)+(n(n+1))/(2*4)+(n(n+1)(n+2))/(2*4*6)+…oo)

If the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

If the sum of the series 1+(3)/(2)+(5)/(4)+(7)/(8)+……+((2n-1))/((2)^(n-1)) is f(n) , then the value of f(8) is

Prove that 5.C_(0) +5^(2).(C_(1))/(2) +5^(3).(C_(2))/(3)+…+5^(n+1).(C_(n))/(n+1)=(6^(n+1)-1)/(n+1) Hence show that 5.C_(0) +(5^(2))/(2).C_(1)+(5^(3))/(3).C_(2)+….+(5^(11))/(11).C_(10)=(6^(11)-1)/(11)

lim_ (n rarr oo) (((n ^ (5) +2) ^ ((1) / (4))) - ((n ^ (2) +1) ^ ((1) / (3))) ) / ((n ^ (4) +2) ^ ((1) / (5)) - (n ^ (3) +1) ^ ((1) / (2))) is