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If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo...

If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+oo,` prove that (x y)/z=(a b)/c

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If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo, prove that (x y)/z=(a b)/c

"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).

If A=1+r^a+r^(2a)+ to oo and B=1+r^b+r^(2b)+oo , prove that r=((A-1)/A)^(1//a)=((B-1)/B)^(1//b)

If x = r sin A cos B, y = r sin A sin B and z = r cos A, then prove that : x^(2) + y^(2) + z^(2) = r^(2)

If x=1+a+a^2+oo,w h e r e|a|<1a n dy=1+b+b^2+oo,w h e r e|b|<1. prove that: 1+a b+a^2b^2+oo=(x y)/(x+y-1)

If a = sum_(r=1)^(oo) 1/(r^(2)), b = sum_(r=1)^(oo) 1/((2r-1)^(2)), then (3a)/b is equal to _____

If x = r cos A cos B, y = r cos A sin B and z = r sin A, show that : x^(2) + y^(2) + z^(2) = r^(2)

In Figure, C D\ || A E\ a n d\ C Y || B A . (i) Name a triangle equal in area of triangle \ C B X (ii) Prove that a r\ (triangle \ Z D E)=\ a r\ (triangle \ \ C Z A) (iii) Prove that a r\ ( B C Z Y)=a r\ (triangle \ E D Z) .

If sum_(r=1)^(oo) (C^r)/(r!) =1 then C =

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Prove that 6^(1//2)xx6^(1//4)xx6^(1//8)...oo=6.

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  2. Three numbers are in G.P. whose sum is 70. If the extremes be each mul...

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  3. If x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n d z=c+c/(r^2)+c/(r^4)+o...

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  4. Find the sum 1+4+13+40+121+dot

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  5. If each term of an infinite G.P. is twice the sum of the terms foll...

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  6. The sum to n terms of series 1+(1+1/2+1/(2^2))+(1+1/2+1/(2^2)+1/(2^3))...

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  7. Find the sum of the following series: (sqrt(2)+1)+1(sqrt(2)-1)+..........

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  8. If the set of natural numbers is partitioned into subsets S1={1},S2={2...

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  9. If p(x)=(1+x^2+x^4++x^(2n-2))//(1+x+x^2++x^(n-1)) is a polomial in x ,...

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  10. If the sum of the squares of the first n natural numbers exceeds theri...

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  11. If f is a function satisfying f(x+y)=f(x)xxf(y) for all x ,y in N suc...

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  12. If sum(r=1)^n tr=n/8(n+1)(n+2)(n+3), then find sum(r=1)^n1/(tr)dot

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  13. Find the sum to n terms of the series :1xx2xx3 + 2xx3xx4 + 3xx4xx5 + ....

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  14. If the sum to infinity of the series 3+(3+d)1/4+(3+2d)1/(4^2)+......oo...

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  15. Find the sum to infinity of the series 1^2+2^2x+3^2x^2+oodot

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  16. If a ,b ,c ,d are in G.P., then prove that (a^3+b^3)^(-1),(b^3+c^3)^(-...

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  17. Find the sum of the series 1-3x+5x^2-7x^3+ ton terms.

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  18. In a geometric progression consisting of positive terms, each term ...

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  19. If the A.M. between two numbers exceeds their G.M. by 2 and the GM. ...

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  20. The AM of teo given positive numbers is 2. If the larger number is inc...

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