Pyramid Investigations 5 – Fifty Tall

It's equal to $2\times(1+2+3+4+5+... ...+40+41+42+44+50)-50$ = $(51\times50)-50$

= $50\times50$ = $\boxed{2500}$

${ n }^{ 2 }={ 50 }^{ 2 }=2500$

Refer to the solution of this problem which suggests that $1+2+3+..+(n-1)+n+(n-1)+...+3+2+1=n^2$ .

Using this fact, we can solve the problem easily like this ---->

$1+2+3+....+49+50+49+.....+3+2+1=50^2=\boxed{2500}$

50^2=2500

$1 + 2 + 3 + \cdots + 49 + 50 + 49 + \cdots + 3 + 2 + 1 = ( 1 + 2 + \cdots + 49 ) \times 2 + 50 = { ( 50 \times 24 ) + 25 } \times 2 + 50 = ( 1200 + 25 ) \times 2 + 50 = 1225 \times 2 + 50 = 2450 + 50 = \boxed { 2500 }$

It's pretty easy. All you have to do is square the middle number of the expression , which is 50 over here.

Probably it's not the best, but I solved this question this way: using the Gauss sum, the sum of 1 + 2 + 3 + ... + 50 = 1275. Then, 1 + 2 + 3 + ... + 48 = 1176. The sum 49 + 1176 = 1225. So, 1275 + 1225 = 2500.

$50^2=2500$

sum of n term of series 1+2+3+------------- is n(n+1)/2 so 49 50/2 + 50 + 49 50/2

Having this succession 1+2+3+4 ....... 49+50+49 ..........+4+3+2+1 +1+2+3+4 +(n–1) + n ....... 49+50+49........ +(n–1) + n ..... +4+3+2+1 = n^2 50^2 = 2500

2500 !.

50^2 gives 2500

50(50+1)/2+49(49+1)/2=(50/2)(51+49)=50*100/2=50^2=2500

50^2=2500

We know that from the previous problems, the pyramids follow the pattern of n^2. Hence, taking the middle no 50 as 50^2 =2500 is the answer we get.

2(1+2+3+.........................+49)+50 will be2500

50*50=2500

(x-2)+(x-1)+x+(x-2)+(x-1)= X^2

It is just the square of 50 the highest term in the sequence.

n=50 thus n^2=2500

Dumb, dumb, dumb...2500.

50^2=2500

A famous mathmatician said, to find the sum of numbers: (first number x last number) x number of numbers divided by 2. So simply use this equation to find the sum until 50 (1+50)x 50 Divided by 2 =1275 Than because you already have 50, Find the sum of numbers between 1 and 49 (1+49)x49 Dixided by 2 =1225 Than add 1275+1225 =2500

since we know that 1+2+...+(n+1)+n+(n+1)+...+2+1=n^2 by comparing given equation and above equation we find that n=50 so 50^2=2500

50^2=2500

Total nos are from 1 to 50 in acsending ,than in decending so sum is 50X50 =2500 Ans K.K.GARG.India

sum of n no`s upto n= n (n+1)/2; so solution is 2 (49*(49+1)/2) + 50 = 2500

Mid of the number = 50 So, 50^2 = 2500