Home
Class 12
MATHS
Using the principle of finite Mathematic...

Using the principle of finite Mathematical Induction prove the following:
(iv) `a+ar+ar^(2)+……..+"n terms" = (a(r^(n)-1))/(r-1) , r != 1`.

Answer

Step by step text solution for Using the principle of finite Mathematical Induction prove the following: (iv) a+ar+ar^(2)+……..+"n terms" = (a(r^(n)-1))/(r-1) , r != 1. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • IPE:MARCH-2019 (AP)

    SRISIRI PUBLICATION|Exercise SECTION - B|7 Videos
  • IPE:MARCH-2018[TS]

    SRISIRI PUBLICATION|Exercise SECTION-C (LAQs)|8 Videos
  • IPE:MARCH-2019(AP)

    SRISIRI PUBLICATION|Exercise SECTION-C|6 Videos

Similar Questions

Explore conceptually related problems

Using the principle of finite Mathematical Induction prove the following: (vi) 2+3.2+4.2^(2)+………."upto n terms" = n.2^(n) .

Using the principle of finite Mathematical Induction prove the following: (iii) 1/(1.4) + 1/4.7 + 1/7.10 + ……… + "n terms" = n/(3n+1) .

Using the principle of finite Mathematical Indcution prove that 2.3 + 3.4 + 4.5 + ……."upto n terms" = (n(n^(2)+6n+11))/(3) .

Using the principle of finite Mathematical Induction prove the following: (v) 3.5^(2n+1)+2^(3n+1) is divisible by 17, AA n in N .

Prove that a+ar+ar^2+.......+n "terms" =(a(r^n+1))/(r-1),r ne 1

Using the principle of finite Mathematical Induction prove that 1^(2)+(1^(2)+2^(2))+(1^(2)+2^(2)+3^(2)) + "n terms" = (n(n+1)^(2)(n+2))/(12), AA n in N .

Using the principle of finite Mathematical Induction prove that 1^2+(1^2+2^2)+(1^2+2^2+3^2)+.......n terms =(n(n+1)^2(n+2))/12,foralln in N

Using the principle of finite Mathematical Induction prove that 1.2.3+2.3.4+3.4.5.+………… upto n terms = n(n+1)(n+2)(n+3))/4,for all n in N

Using the principle of Mathematical Induction, Show that 49^n+16n-1 is divisible by 64, forall n in N .

Using the principle of Mathematical Induction , forall n in N , prove that 1^2+2^2+3^2+.....n^2=(n(n+1)(2n+1))/6