Home
Class 11
MATHS
मान लीजिए कि x=1+a+a^(2)+... ओर y=1+...

मान लीजिए कि `x=1+a+a^(2)+... ` ओर `y=1+b+b^(2)+..., ` जहाँ ` |a|lt 1` ओर `|b|lt1` है । सिद्ध कीजिए कि
`1+ab+a^(2)b^(2)+...=(xy)/(x+y-1)`

Promotional Banner

Similar Questions

Explore conceptually related problems

Let x=1+a +a^(2) + ….. And y= 1 + b + b^(2)+ …… where |a| lt 1 and |b| lt 1 . Prove that: 1+ ab + a^(2)b^(2) +…… =(xy)/(x+y-1) .

If x = 1 + a + a^(2) + …. infty " , " y = 1 + b + b^(2) + …. infty, " " |a| lt 1 , |b| lt 1, then 1 + ab + a^(2) b^(2) + ….. infty =

If x = 1 + a + a^(2) +… oo (-1 lt a lt 1) and y = 1 + b + b^(2)+ … oo (-1 lt b lt 1) , prove that, 1+ab + a^(2)b^(2)+ … oo = (xy)/(x+y - 1)

Let x=1+a+a^(2)+... and y=1+b+b^(2)+..., where |a|<1 and . Prove that 1+ab+a^(2)b^(2)+...=(xy)/(x+y-1)

|a| lt 1 and |b| lt 1, x=1 + a + a^(2) + ……. and y=1 + b + b^(2) + …..,Prove that, 1 + ab + a^(2) b^(2) + ….= (xy)/(x+y-1)

सिद्ध कीजिए कि 2tan^(-1)sqrt((b)/(a))=cos^(-1)((a-b)/(a+b))

If x=1+a+a^(2)+...oo, a lt 1 and y=1+b+b^(2)+...oo, b lt 1, then 1+ab+a^(2)b^(2)+...oo :

If =1+a+a^(2)+oo, where |a|< 1andy =1+b+b^(2)+oo, where |b|<1 prove that: 1+ab+a^(2)b^(2)+oo=(xy)/(x+y-1)

If x=1 +a + a^2+…. to oo , where |a| lt1 and y=1+b+b^2+… to oo , where |b|lt1 , prove that 1+ab+a^2b^2+… to oo=((xy)/(x+y-1))