Q. the sum of the infinite series `1+2/3*1/2+2/3*5/6*1/2^2+2/3*5/6*8/9*1/2^3+....,` is

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

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo

Prove that : Find the sum of the infinite series 1+(2)/(3).(1)/(2)+(2.5)/(3.6)((1)/(2))^(2)+(2.5.8)/(3.6.9)((1)/(2))^(3)+......oo

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sum of different series. Q. Sum of infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo is

Let n is a rational number and x is a real number such that |x|lt1, then (1+x)^(n)=1+nx+(n(n-1)x^(2))/(2!)+(n(n-1)(n-2))/(3!).x^(3)+ . . . This can be used to find the sum of different series. Q. Sum of infinite series 1+(2)/(3)*(1)/(2)+(2)/(3)*(5)/(6)*(1)/(2^(2))+(2)/(3)*(5)/(6)*(8)/(9)*(1)/(2^(3))+ . . .oo is

Find the sum of the following infinite series 1/2(1/5)^2+2/3(1/5)^3+3/4(1/5)^4+

Find the sum of the infinite series. 1/(1.2.3)+1/(2.3.4)+1/(3.4.5)+...