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what is the sum of no.s in the mth group when m consecutive natural no.s are clubbed in the mth group. {1};{2,3};{3,4,5};.......

what is the sum of no.s in the mth group when m consecutive natural no.s are clubbed in the mth group.
{1};{2,3};{3,4,5};.......

Grade:11

2 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
7 years ago
The mth group will start with m and have the following m consecutive numbers in it
{m,m+1,m+2,...,2m-2,2m-1}
So the sum would be
S = m+(m+1)+...+(2m-1) = m\times m + 0+1+2+...+m-1
S = m^2 + (m-1)m/2
Prabhakar ch
577 Points
7 years ago
S= m2+(m-1)m/2

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