1guess b
S=r=1Σ20471/r
options
a)5<S<6
b)S>6
c)11<S<12
d)S<11
answer with proof
if its not in syllabus then tell
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11 Answers
62S=r=1Σ20471/r
try this...
1/3+1/4 > 2.1/4 = 1/2
1/5+1/6+1/7+1/8 > 4.1/8 = 1/2
...
....
...
1/1025+....1/2047 > 1/2
thus taking the sum,
S > 1+1/2+ 1/2.... 1/2 (1/2 will be there 11 times)
so > 6.5
62you can also say one more inequality
try this...
1/2+ 1/3 < 2.1/2 = 1
1/4 + 1/5+1/6+1/7 < 4.1/4 = 1
...
....
...
1/1024+....1/2047 <1
thus taking the sum,
S < 1+1+...1 (11 times)
so S< 11
21ANS : B
REFER THIS LINK FOR SOLUTION
U'LL get S>6.5
http://subhanilchoudhury.blogspot.com/2007/05/harmonic-progressionhp.html
21sorry sir, aapka post nahi padha....
the link gives pretty much the same solution...
11why do we group terms like these
is it a particular method ??
and is this in the syllabus
62@tapan:
it is ok..
but you have to see that D is also a soluton! both B and D
@subash.: You can say that this is because it is a trick! the motivation comes from the fact that between 1/2n and 1/2n+1 the terms will all have values < 1/2n and > 1/2n+1 and interestingly they will be 2n terms!
21yah.... I thot it was straight type MCQ, dinno it was multiple answered....