`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))`

The sum of the series 2/3+8/9+(26)/(27)+(80)/(81)+ to n terms is (a) n-1/2(3^(-n)-1) (b) n-1/2(1-3^(-n)) (c) n+1/2(3^n-1) (d) n-1/2(3^n-1)

2.5+3.8+4.11+.....+ upto n terms =n(n^(2)+4n+5), n in N

Prove the following by using the principle of mathematical induction for all n in N (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)+............1/((3n-1)(3n+2))=n/((6n+4)) forall n in N.

Prove the following by using the principle of mathematical induction for all n in Nvdots(1)/(2.5)+(1)/(5.8)+(1)/(8.11)+...+(1)/((3n-1)(3n+2))=(n)/((6n+4))=(n)/((6n+4))

The sum of the series (2)/(3)+(8)/(9)+(26)/(27)+(80)/(81)+ to n terms is n-(1)/(2)(3^(-n)-1)(b)n-(1)/(2)(1-3^(-n))(c)n+(1)/(2)(3^(n)-1)(d)n-(1)/(2)(3^(n)-1)

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

If n is a non zero rational number then show that 1 + n/2 + (n (n - 1))/(2.4) + (n(n-1)(n - 2))/(2.4.6) + ….. = 1 + n/3 + (n (n + 1))/(3.6) + (n (n + 1) (n + 2))/(3.6.9) + ….

The value of C_1/2+C_3/4+C_5/6+………. is equal to (A) (2^n=1)/(n-10 (B) 2^n/(n=1) (C) (2^n+1)/(n+1) (D) (2^n-1)/(n+1)