A number theory problem by Charles Curran

Number Theory Level 1

What is 1+2+3+4+5+6+7+8+..........+50?

1233 101 1275 1250

Charles Curran by Charles Curran , 47, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Arulx Z
Dec 11, 2015

You can use the formula n ( n + 1 ) 2 \frac { n\left( n+1 \right) }{ 2 } .

Working -

S = 1 + 2 + 3 + … + 49 + 50 S = 50 + 49 + 48 + … + 2 + 1 S + S = 51 + 51 + 51 + … + 51 + 51 \begin{matrix} S & = & 1 & + & 2 & + & 3 & + & \dots & + & 49 & + & 50 \\ S & = & 50 & + & 49 & + & 48 & + & \dots & + & 2 & + & 1 \\ S+S & = & 51 & + & 51 & + & 51 & + & \dots & + & 51 & + & 51 \end{matrix}

We know that

51 + 51 + 51 + ⋯ + 51 + 51 ⏟ 50 terms \underbrace { 51+51+51+\dots +51+51 }_{ 50\quad \text{terms} }

So

2 S = 50 ⋅ 51 S = 25 ⋅ 51 S = 1275 2S=50\cdot 51\\ S=25\cdot 51 \\ S = 1275

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

Ah, the Gauss approach to summing an AP.

FYI If you want to arrange the columns, use an array:

1 2 3 4 5 \begin{array} { l l l } 1 & 2 & 3 \\ & 4 & 5 \\ \end{array}

Calvin Lin Staff - 5 years, 5 months ago

Log in to reply

Thanks! I have fixed my answer.

Arulx Z - 5 years, 5 months ago
Charles Curran
Nov 21, 2015

51 digits. The average is 25. 51x25=1,275

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...