Home
Class 12
MATHS
1+3+5+.. . .+(2 n-1)=...

`1+3+5+.. . .+(2 n-1)=`

A

`n^(2)+1`

B

`2 n`

C

`n^(2)`

D

` n^(2)-1`

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|32 Videos

  • MATHEMATICAL REASONING

    HIMALAYA PUBLICATION|Exercise Question Bank|97 Videos

Similar Questions

Explore conceptually related problems

Prove the following by the principle of mathematical induction: \ 1. 3+2. 4+3. 5++(2n-1)(2n+1)=(n(4n^2+6n-1))/3

Using the principle of mathematical induction to prove that int_(0)^(pi//2)(sin^2nx)/(sinx)dx=1+(1)/(3)+(1)/(5)+.....+(1)/(2n-1)

Knowledge Check

  • sum_(k=1)^(5) (1^(3)+2^(3)+.. ..+k^(3))/(1+3+5+.. ..+(2 k-1))=

    A
    1: 22.5
    B
    2: 24.5
    C
    3: 28.5
    D
    4: 32.5

  • The value of ""2^n[1.3.5 ..........(2n-3)(2n-1)] is

    A
    `((2n)i)/(n!)`
    B
    `((2n)i)/(2^n)`
    C
    `(n!)/((2n)!)`
    D
    None of these

  • 1 . 3+3 . 5+5 . 7+.. . . to n terms =

    A
    1)` (n)/(5) (3 n^(2)+7 n+5)`
    B
    2)`(n)/(2)(2 n^(2)+3 n+1)`
    C
    3)`(n)/(3)(4 n^(2)+6 n-1)`
    D
    4)`(n)/(4)(4 n^(2)+6 n+2)`

    • Similar Questions

    Explore conceptually related problems

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

    Prove that by using the principle of mathematical induction for all n in N : 1.2.3+ 2.3.4+ ....+ n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/(4)

    If n in N then 3 . 5^(2 n+1)+2^(3 n+1) is divisible by

    Let S_(n) = ( 1)/( 1^(3)) + ( 1+2)/( 1^(3) + 2^(3)) +"...." + ( 1+ 2 + "...." + n)/(1^(3) +2^(3)"...."+n^(3)), n = 1,2,3,"....." , Then S_(n) is not greater than :

    For a positive integer n, let a(n)=1+(1)/(2)+(1)/(3)+(1)/(4)+ . . .+(1)/(2^(n)-1) Then:

    Home
    Profile