Home
Class 11
MATHS
If Sp denotes the sum of the series 1+r^...

If `S_p` denotes the sum of the series `1+r^p+r^(2p)+ toooa n ds_p` the sum of the series `1-r^(2p)r^(3p)+ tooo,|r|<1,t h e nS_p+s_p` in term of `S_(2p)` is `2S_(2p)` b. `0` c. `1/2S_(2p)` d. `-1/2S_(2p)`

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise All Questions|9 Videos

  • STRAIGHT LINES

    CENGAGE ENGLISH|Exercise All Questions|491 Videos

Similar Questions

Explore conceptually related problems

If S_p denotes the sum of the series 1+r^p+r^(2p)+... tooo and S_(p') the sum of the series 1-r^p+r^(2p)-... tooo, prove that S_(p)+S_(p')=2S_(2p)dot

Sum of the series sum_(r=1)^(n) (r^(2)+1)r! is

If S be the sum, p the product and R the sum of the reciprocals of n terms of a G.P., then (S/R)^n is equal to

If the sum of the coefficients in the expansion of (q+r)^(20)(1+(p-2)x)^(20) is equal to square of the sum of the coefficients in the expansion of [2rqx-(r+q)*y]^(10) , where p , r , q are positive constants, then

If S is the sum, P the product and R the sum of the reciprocals of n terms in G.P., prove that P^(2)= ((S)/(R))^(n) .

in an AP , S_p=q , S_q=p and S_r denotes the sum of the first r terms. Then S_(p+q)=

If the lengths of the perpendiculars from the vertices of a triangle ABC on the opposite sides are p_(1), p_(2), p_(3) then prove that (1)/(p_(1)) + (1)/(p_(2)) + (1)/(p_(3)) = (1)/(r) = (1)/(r_(1)) + (1)/(r_(2)) + (1)/(r_(3)) .

If in an A.P., S_n=n^2p and S_m=m^2p , where S_r denotes the sum of r terms of the A.P., then S_p is equal to 1/2p^3 (b) m n\ p (c) p^3 (d) (m+n)p^2

If r_(1), r_(2), r_(3) in triangle be in H.P., then the sides are :

if S is the sum , P the product and R the sum of reciprocals of n terms in G.P. prove that P^2 R^n=S^n

CENGAGE ENGLISH-SEQUENCES AND SERIES-All Questions
  1. Let {tn} be a sequence of integers in G.P. in which t4: t6=1:4 and t2+...

    Text Solution

    |

  2. If x ,2y ,3z are in A.P., where the distinct numbers x ,y ,z are in G....

    Text Solution

    |

  3. If Sp denotes the sum of the series 1+r^p+r^(2p)+ toooa n dsp the sum ...

    Text Solution

    |

  4. If x ,y ,z are real and 4x^2+9y^2+16 z^2-6x y-12 y z-8z x=0,t h e nx ,...

    Text Solution

    |

  5. If a1, a2, ,an are in H.P., then (a1)/(a2+a3++an),(a2)/(a1+a3++an), ...

    Text Solution

    |

  6. If H1, H2, ,H(20) are 20 harmonic means between 2 and 3, then (H1+2)/...

    Text Solution

    |

  7. A pack contains n cards numbered from 1 to n. Two consecutive numbered...

    Text Solution

    |

  8. Let an=16 ,4,1, be a geometric sequence. Define Pn as the product o...

    Text Solution

    |

  9. If he equation x^3+a x^2+b x+216=0 has three real roots in G.P., then ...

    Text Solution

    |

  10. Let Tr be the rth term of an A.P., for r=1,2,3,..... If for some pos...

    Text Solution

    |

  11. If an=3/4-(3/4)^2+(3/4)^3+...(-1)^(n-1)(3/4)^n and bn=1-an, then find ...

    Text Solution

    |

  12. For a positive integer n let a(n)=1+1/2+1/3+1/4+.....+1/((2^n)-1)dot T...

    Text Solution

    |

  13. If x >1,y >1,a n dz >1 are in G.P., then 1/(1+lnx),1/(1+l ny)a n d1/(1...

    Text Solution

    |

  14. .Let a1, a2,............ be positive real numbers in geometric progr...

    Text Solution

    |

  15. about to only mathematics

    Text Solution

    |

  16. If a ,b ,c are in A.P. and a^2, b^2, c^2 are in H.P., then prove tha...

    Text Solution

    |

  17. Let a ,b be positive real numbers. If a, A1, A2, b be are in arithmeti...

    Text Solution

    |

  18. The sum of an infinite G.P. is 57 and the sum of their cubes is 9747, ...

    Text Solution

    |

  19. If a^2+b^2,a b+b c and b^2+c^2 are in G.P., then a ,b ,c are in a. A.P...

    Text Solution

    |

  20. If y^2=x za n da^x=b^y=c^z , then prove that (log)6a=(log)c bdot

    Text Solution

    |