Home
Class 12
MATHS
If a = underset(55 "times")underbrace(11...

If `a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3)+10^(4) and c=1+10^(5)+10^(10)+.+10^50` then prove that a=bc

A

a+b+c

B

a=bc

C

b=ac

D

c=ab

Text Solution

Verified by Experts

The correct Answer is:
B
`a=1+10+10^(2)+….+10^(54)`
`=(10^(55)-1)/(10-1)=(10^(55)-1)/(10^(5)-1)xx(10^(5)-1)/(10-1)=bc`
Promotional Banner

Topper's Solved these Questions

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( MULTIPLE CORRECT ANSWER TYPE )|66 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise EXERCIESE ( LINKED COMPREHENSION TYPE )|60 Videos

  • PROGRESSION AND SERIES

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERICISE 5.9|9 Videos

  • PROBABILITY II

    CENGAGE PUBLICATION|Exercise MULTIPLE CORRECT ANSWER TYPE|6 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE PUBLICATION|Exercise Archives (Numerical Value Type)|3 Videos

Similar Questions

Explore conceptually related problems

(1-4 sin 10^(@) sin70^(@))/(2 sin 10^(@))=

Solve:- 10^5 xx 10^2 = ?

If (10)^9 + 2(11)^1 (10)^8 + 3(11)^2 (10)^7+..+10(11)^9 = k(10)^9 then k is equal to :

Prove that, tan 35^(@) + tan 10^(@) + tan35^(@) tan 10^(@) = 1

If underset(xrarroo)"lim"((1+x)^(10)+(x+2)^(10)+....+(x+100)^(10))/(x^(10)+10^(10)) =K^(2) , then the value of K will be -

If 10^(9)+2(11)^(1)(10)^(8)+3(11)^(2)(10)^(7)+...+10(11)^(9)=k(10)^(9) , then k is equal to -

Evaluate : underset(x to oo)(Lt)((x+1)^10+(x+2)^10+.....+(x+100)^10)/x^10

Let's from the numbers from their expanded from given below:- 8 xx 10^4 + 2 xx 10^3 + 3 xx 10^2 + 6 and 9 xx 10^4 + 5 xx 10^3 + 6 xx 10^2 + 7 xx 10

The rate constant of a reaction 1.5xx10^(7)s^(-1) " at " 50^(@)C and 4.5xx10^(7)s^(-1) at 100^(@)C Evaluate the Arrhenius parameters A and E_(a)

At the three vertices of an equilateral triangle of side 10 cm, +1.0 xx 10^(-7)C, +2.0 xx 10^(-7)C and -4.0 xx 10^(-7)C charges are placed. Calculated the potential energy of the system of these charges.

CENGAGE PUBLICATION-PROGRESSION AND SERIES-EXERCIESE ( SINGLE CORRECT ANSWER TYPE )
  1. Consider the ten numbers a r ,a r^2, a r^3, ,a r^(10)dot If their sum...

    Text Solution

    |

  2. If x ,y ,a n dz are distinct prime numbers, then (a).x , y , a n dz ma...

    Text Solution

    |

  3. If a = underset(55 "times")underbrace(111.....1), b= 1+10+10^(2)+10^(3...

    Text Solution

    |

  4. Let an be the nth therm of a G.P of positive numbers .Let Sigma(n=1)^(...

    Text Solution

    |

  5. The sum of 20 terms of a series of which every even term is 2 times ...

    Text Solution

    |

  6. Let a in (0,1) satisfies the equation a^(2008)-2a+1=0v a l u e s(s)toS...

    Text Solution

    |

  7. In a geometric series, the first term is a and common ratio is rdot If...

    Text Solution

    |

  8. Let Ssub(0,pi) denote the set of values of x satisfying the equation 8...

    Text Solution

    |

  9. If sec alpha and alpha are the roots of x^2-p x+q=0, then (a) p^2=q(q-...

    Text Solution

    |

  10. The value of 0. 2^(logsqrt(5)1/4+1/8+1/(16)+) is 4 b. log4 c. log2 d....

    Text Solution

    |

  11. If x=9^(1/3) 9^(1/9) 9^(1/27) ...->∞ , y= 4^(1/3) 4^(-1/9) 4^(1/27) ....

    Text Solution

    |

  12. The value of x that satisfies the relation x=1 -x+x^2-x^3+x^4-x^5+….oo...

    Text Solution

    |

  13. If S dentes the sum to infinity and Sn the sum of n terms of the serie...

    Text Solution

    |

  14. The first term of an infinite geometric series is 21. The second term ...

    Text Solution

    |

  15. The sum of an infinite G.P. is 57 and the sum of their cubes is 9457 ,...

    Text Solution

    |

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

    Text Solution

    |

  17. If the sum to infinity of the series 1+2r+3r^2+4r^3+ is 9/4, then valu...

    Text Solution

    |

  18. Find the sum of the series 1+4/5+7/(5^2)+10/(5^3)+...

    Text Solution

    |

  19. The sum of 0.2+0.004+0. 00006+0. 0000008+... to oo is

    Text Solution

    |

  20. The positive integer n for which 2xx2^2xx+3xx2^3+4xx2^4++nxx2^n=2^(n+1...

    Text Solution

    |