Home
Class 12
MATHS
If 1.3+2.3^(2)+3.3^(3)+ . . .=n3^(n)=((2...

If 1.3+2.`3^(2)+3.3^(3)+ . . .=n3^(n)=((2n-1)3+b)/(4)`, then a and b are respectively:

Text Solution

Verified by Experts

The correct Answer is:
a = n + 1, b = 3
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • PROGRESSIONS

    ML KHANNA|Exercise PROBLEM SET - 5 (MULTIPLE CHOICE QUESTIONS) |92 Videos
  • PROGRESSIONS

    ML KHANNA|Exercise PROBLEM SET - 5 (Assertion/Reason) |1 Videos
  • PROGRESSIONS

    ML KHANNA|Exercise PROBLEM SET - 4 (TRUE AND FALSE) |1 Videos
  • PROBABILITY

    ML KHANNA|Exercise MISCELLANEOUS EXERCISE|6 Videos
  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Self Assessment Test (Multiple Choise Questions)|34 Videos

Similar Questions

Explore conceptually related problems

1.3+2.3^(2)+3.3^(3)+............+n.3^(n)=((2n-1)3^(n+1)+3 )/(4)

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

Using the principle of mathematical induction prove that : the 1.3+2.3^(2)+3.3^(3)++n.3^(n)=((2n-1)3^(n+1)+3)/(4) for all n in N.

1^(3)+2^(3)+3^(3)+...+n^(3)=n^(2)((n+1)^(2))/(4)

1^(3)+2^(3)+3^(3)+....+n^(3)=((n(n+1))/(2))^(2)

(1^(3)+2^(3)+...+n^(3))/(1+3+5+...+(2n-1))=((n+1)^( 2))/(4)

1.2.3+2.3.4++n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

Prove the following by using the principle of mathematical induction for all n in Nvdots1.3+2.3^(2)+3.3^(3)+...+n.3^(n)=((2n-1)3^(n+1)+3)/(4)

(2.3^(n+1)+7.3^(n-1))/(3^(n+1)-2((1)/(3))^(1-n))=

1.3+2.4+3.5+....+n(n+2)=(n(n+1)(2n+7))/(6)