Summing Singles

We have $1+2+3+4+5+6+7+8+9$ $=(1+9)+(2+8)+(3+7)+(4+6)+5$ $=10+10+10+10+5$ $=\boxed{45}.$

I have another solution for this problem. Since arithmetic progression and total number is odd, you can look the median number. The median number of that problem is $5$ .

You can manipulate them using that number, so look at below:

$1 + 2 + 3 + 4 + \boxed{5} + 6 + 7 + 8 + 9$

$=(5-4) + (5-3) + (5-2) + (5-1) + \boxed{5} + (5+1) + (5+2) + (5+3) + (5+4)$

$= 5 + 5 + 5 + 5 + \boxed{5} + 5 + 5 + 5 + 5$

$= 5*9$

$=\boxed{45}$

Use method of Gausean pairing, $10*9/2=45$

We can use the formula for sum of 'n' terms of an AP, but this is a better approach:-

$1+2+3+4+5+6+7+8+9=45$ . BANG!!

Using formula for finding sum of first 'n' natural numbers i.e. n(n+1)/2 .

putting n=9 in above formula we get 45.

9+(8+1)+(7+2)+(6+3)+(5+4) =9+9+9+9+9 =45

simply add

Lowest Number of the Equation + Highest Number of the Equation 1 + 9 = 10 Divide the amount numbers in the equation by 2 9 / 2 = 4.5 10 x 4.5 = 45

= (1 + 2) + (3 + 4) + (5 + 6) + (7 + 8) + 9 = (3) + (7) + (11) + (15) + 9 = (3 + 7)+ (11 + 15) + 9 = 10 + 26 + 9 = 45 Not the easiest way but different.

Simplest way... with both odd and even integers and any arithmetic sequence... take total amount, not sum, of integers and multiply by mean of sequence

Use the formula- n (n+1)/2.

Thus 1+2+..+9 = 9 x 10/2 =90/2 =45

N n+1(n is alast number)/2 So,9 10/2=90/2=45 So it is very easy Or add all number so it is easy

Dont use calculator. Sheesh

Arithmetic solution: n/2(a1+an) =9/2 (1+9) =45

1+2+3+4+5+6+7+8+9= (1+2)=3+3=6+4=10+5=15+6=21+7=28+8=36+9=45