Sumz

Number Theory Level 1

the sum of first n odd numbers=?

n

{ n }^{ 2 }

{ n }^{ 3 }

{ n }^{ 2 }+2n

3 solutions

Anuj Shikarkhane
Jul 22, 2014

Take the odd numbers 1,3,5,7.Their sum is 16 and the number of terms is 4.So sum is $n^2$ .Now check this with some more numbers. 1,3,5,7,9.Sum is 25.Number of terms are 5.So $5^2$ .Therefore the answer is $n^2$ .

yes the problem may only ask you the final result but its requirement is also to do the whole process correctly. What I am telling is you have to prove that this true even for the 10000000000... term (you cant actually check this).

Sathvik Acharya - 4 years, 3 months ago

William Isoroku
Aug 2, 2014

(first term + last term x the number of terms)/2 = (1+2n-1)(n)/2, when simplified is n^2

Azadali Jivani
Aug 12, 2015

(n/2)(2f+(n-1)d)..........f is first term, d is difference of two terms,
=(n/2)(2*1 + (n-1)2)
=(n/2)(2n)
=(2n^2) /2 = n^2 (Ans.)

yes that's the perfect solution mate, but there is no up vote for this solution for some reason and there are up votes for solutions that are not completely right.

Sathvik Acharya - 4 years, 3 months ago

Sumz

3 solutions

0 pending reports