If `x=(1)/(5)+(1.3)/(5.10)+(1.3.5)/(5.10.15)+….oo` then find `3x^(2)+6x.`

If x = (1.3)/(3.6) + (1.3.5)/(3.6.9) + (1.3.5.7)/(3.6.9.12) + ….. then prove that 9x^2 + 24x = 11

Show that (3.5)/(5.10) + (3.5.7)/(5.10.15) + (3.5.7.9)/(5.10.15.20)+ …..oo = (5sqrt5)/(3 sqrt3) - 8/5

If x = (1)/(1.2) + (1)/(3.4) + (1)/(5.6) …….oo, and y = 1 - (1)/(2.3) - (1)/(4.5) - (1)/(6.7)…….oo , then

1+ (1)/(10^2) + (1.3)/(1.2). (1)/(10^4) + (1.3.5)/(1.2.3) . (1)/(10^6) + …… oo =

cos x +(1)/(3)cos^(3)x+(1)/(5)cos^(5)x+…..oo=

If f(x)=(x^(2))/(1.2)-(x^(3))/(2.3)+(x^(4))/(3.4)-(x^(5))/(4.5)+..oo then

Find the sum of the infinite series (7)/(5)(1+(1)/(10^(2))+(1.3)/(1.2).(1)/(10^(4))+(1.3.5)/(1.2.3).(1)/(10^(6))+....)

If 2|(3, 4),( 5,x)|+|(1,y),(0, 1)|=|(7, 0),(10, 5)| , find x-y .

Solve: 2/(5x)-5/(3x)=1/(15)

If x= (1)/(5-x) and x ne 5 , find x^(3) + (1)/(x^(3))