From Power prep again

[abaabeel]

s= 1- 1/2 + 1/3- 1/4 +1/5-1/6+1/7-1/8+1/9-1/10

Col A: S

Col B: 1/2

OA is A. Any short method to solve such questions please?

[deichgraf]

Yes, there is. Regarding S; 1-0,5 = 0,5 From now on, you first add a fraction e.g. 1/3 or 1/5 and after adding a fraction you always substract one fraction +1/3 -1/4 or +1/5 - 1/6.
Since the fraction you substract is always less than the fraction you added before, however you will get a positive rest r, thus r > 0. 1-0,5+r= 0,5 + r.
Clearly 0,5 + r is greater than 0,5. Answer is A.

[abaabeel]

It is still not clear. Can you please expound a bit more?... Thanks in advance

[rose0550]

S={1-1/2}+{1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10}=
1/2+{1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10},
hence S=1/2+a, a=1/3-1/4+1/5-1/6+1/7-1/8+1/9-1/10 and we need to estimate part a,
1/3>1/10,
so the part 'a' will be more than zero, so S>1/2.

[deichgraf]

We should look at s again, setting some braces (its correct because equation does not change), we get:

s= (1- 1/2) + [(1/3- 1/4 ) +(1/5-1/6) +(1/7-1/8)+(1/9-1/10)]
s= 0,5 + [ r ] ---> r is the sum in general, its absolute value does not matter!

Now, look at inner braces of r. Since 1/3>1/4 and 1/5>1/6 (and so on) you always substract a smaller fraction from a bigger one! Every inner brace is e.g. 1/3-1/4 is more than zero! However, all inner braces are added to each other, clearly r has to be greater than 0, too!

After all 0,5 + r is greater than 0,5 , because r>0 no matter which absolute value it takes...
Hope it becomes clear...

[Riyad Mohammad]

s= 1- 1/2 + 1/3- 1/4 +1/5-1/6+1/7-1/8+1/9-1/10 first 1-1/2 u will get 1/2. Then all the following pairs have a +ve value value so u will get s=1/2+sum so COL A is greater

[abaabeel]

Thank you....It is pretty clear now..