Find `5/1.2.1/3+7/2.3.1/3^2+9/3.4.1/3^3+11/4.5.1/3^4+…………to n` terms

The sum of n terms of the series 5/1.2.1/3+7/2.3.1/3^2+9/3.4.1/3^3+11/4.5.1/3^4+.. is (A) 1+1/2^(n-1).1/3^n (B) 1+1/(n+1).1/3^n (C) 1-1/(n+1).1/3^n (D) 1+1/2n-1.1/3^n

Find (1)/(3)+(1)/(2.3^(2))+(1)/(3.3^(3))+(1)/(4.3^(4))+….oo=?

The sum of the series 1+ 2/3+ (1)/(3 ^(2)) + (2 )/(3 ^(3)) + (1)/(3 ^(4)) + (2)/(3 ^(5)) + (1)/(3 ^(6))+ (2)/(3 ^(7))+ …… upto infinite terms is equal to :

Show that 1 + 1/2.(3/5) + (1.3)/(2.4) (3/5)^2 + (1.3.5)/(2.4.6) (3/5)^3 + …… = sqrt([5/2])

The sum to 100 terms of the series 1.2.3. + 2.3.4. + 3.4.5. + …+ n(n + 1) (n+2) + …. is integral multiple of

If the sum of n term of the series (5)/(1.2.3) + (6)/(2.3.4) + ( 7)/(3.4.5)+"…." is a/2 - (n+b)/((n+1)(n+2)) , then

1/(1.2)+(1.3)/(1.2.3.4)+(1.3.5)/(1.2.3.4.5.6)+.....oo

Solve (a) 2/3 + 1/7 (b) 3/10 + 7/15 (c) 4/9 + 2/7 (d) 5/7 + 1/3 (e) 2/5 + 1/6 (f) 4/5 + 2/3 (g) (3/4) (1/3) (h) (5/6) (1/3) (1) 2/3 + 3/4 + 1/2 (1) 1/2 + 1/3 = 1/6 (k) (1) 1/3 + (3) 2/3 (1) (4) 2/3 +(3) 1/4 (m) ((16)/5))(7/5)

If A=[[2/3, 1, 5/3],[ 1/3, 2/3, 4/3] ,[7/3, 2, 2/3]] and B=[[2/3, 3/5, 1],[ 1/5, 2/5, 4/5],[ 7/3, 6/5, 2/5]] , then compute 3A - 5B .

Find the sum of the infinite series 1.3/2+ 3.5/2^2+ 5.7/2^3+ 7.9/2^4+.......oo