Question

The sum of 1+3+5+7+.........
upto n
terms is [MP PET 1984]
A) {{(n+1)}^{2}} B) {{(2n)}^{2}} C) {{n}^{2}} D) {{(n-1)}^{2}}

Answer 1

Hi ,

1 + 3 + 5 + 7 + ... + n terms = n²

Sum of first n odd natural numbers = n²

Option ( C ) is correct.

I hope this helps you.

: )

Answer 2

Hey there!

1 + 3 + 5 + 7 + ... + n

= Sum of n odd numbers

= Sum of ' 2n ' natural numbers - Sum of ' n ' even numbers.

[ In 2n natural numbers, there are n even numbers and n odd numbers ]

= 2n(2n+1)/2 - (n)(n + 1 )

= n ( 2n + 1 ) - n ( n + 1 )

= 2n² + n - n² - n

= n²

Therefore, 1 + 3 + 5 + ... + n = n²

Option [ C ] is the required answer!

Hope helped!