+0

# If we use (x+) to indicate the following sum

0
342
4
+281

If we use (x+) to indicate the following sum
1 + 2 + 3 + ... + x
then find the value of k in the following equation
(28+) - (27+) = (k+)

kes1968  Aug 12, 2015

#4
+81077
+10

The sum of the first "k" positive integers is given by :   (k)(k + 1)/2

So  (x +)   where x =  28  is just  (28)(29) /2     and  (x+) where x = 27  is just (27)(28)/2

So we have

(28)(29)/2 -  (270(28)/2        ..... factor out 28/2

[28/2] [ 29 - 27]=

[14] [2]  = 28

And notice that :

1 + 2 + 3 + 4 + 5 + 6 + 7  = 28

So this equals the sum of the first seven positive integers  =  (7)(8)/2  = 56/2 = (7+)

CPhill  Aug 12, 2015
Sort:

#1
+81077
+5

(28+) - (27+) =

(28)(29)/ 2 - (27)(28)/2  =

(28) [ (29) - (27) ] / 2 =

(28/2) (2) = 28  =  (7)(8)/ 2 =   (7+)   ...so k = 7

CPhill  Aug 12, 2015
#2
+281
0

I AN NOT GETTING WHAT YOU HAVE GIVEN PLEASE EXPLAIN YOUR ANS TO ME MORE BRIEFLY

kes1968  Aug 12, 2015
#3
+18835
+10

If we use (x+) to indicate the following sum
1 + 2 + 3 + ... + x
then find the value of k in the following equation
(28+) - (27+) = (k+)

$$\small{\text{ \begin{array}{rcl} (28+)-(27+) = (k+) = 28 &=& S_k \qquad (28+) = S_{28} \quad (27+)=S_{27}\\\\ S_{28}-S_{27} = t_{28} = 28&=&S_k\\\\ S_k &=& t_1 \cdot \dbinom{k}{1} + d\cdot \dbinom{k}{2} \qquad t_1=d=1\\\\ S_k &=& \dbinom{k}{1} + \dbinom{k}{2} = \dbinom{k+1}{2} = 28\\\\ \\ \dfrac{k(k+1)}{2} &=& 28 \\\\ k(k+1) &=& 56\\\\ k^2+k-56&=&0\\\\ \Rightarrow k &=& \dfrac{-1+15}{2} = 7\\\\ \mathbf{S_k = (k+) }& \mathbf{=} & \mathbf{(7+)}\\\\ (7+)=1+2+3+4+5+6+7&=&28 \\ \end{array} }}$$

heureka  Aug 12, 2015
#4
+81077
+10

The sum of the first "k" positive integers is given by :   (k)(k + 1)/2

So  (x +)   where x =  28  is just  (28)(29) /2     and  (x+) where x = 27  is just (27)(28)/2

So we have

(28)(29)/2 -  (270(28)/2        ..... factor out 28/2

[28/2] [ 29 - 27]=

[14] [2]  = 28

And notice that :

1 + 2 + 3 + 4 + 5 + 6 + 7  = 28

So this equals the sum of the first seven positive integers  =  (7)(8)/2  = 56/2 = (7+)

CPhill  Aug 12, 2015

### 29 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details