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Kavya S
Subject: Maths
, asked on 5/1/18
Q). If you have Rs. 250/- to purchase all the four items from one shop, then which shop would it be? Why? Justify your answer. Do you use PMI to analyze your answer?
Answer
0
Ranjan Shivam
Subject: Maths
, asked on 2/1/18
Q. if a, b, c, are in A.P. , then
1
b
+
c
,
1
c
+
a
,
1
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+
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n
(
A
)
A
.
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.
(
B
)
G
.
P
.
(
C
)
H
.
P
.
(
D
)
N
o
n
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o
f
t
h
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s
e
Answer
1
Nura Mohammad
Subject: Maths
, asked on 25/11/17
Q. Prove that
2
n
>
n
f
o
r
a
l
l
p
o
s
i
t
i
v
e
i
n
t
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g
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r
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n
.
Please explain the last line of solution
Answer
1
Nura Mohammad
Subject: Maths
, asked on 25/11/17
How is the underlined step coming?
Answer
1
Nura Mohammad
Subject: Maths
, asked on 25/11/17
Prove the following by the principle of mathematical induction.
2n?>?n2, where?n?is a positive integer such that?n?> 4.
Solution:
Let the given statement be P(n), i.e.,
P(n) : 2n?>?n2?where?n?> 4
For?n?= 5,
25?= 32 and 52?= 25
?25?> 52
Thus, P(n) is true for?n?= 5.
Let P(n) be true for?n?=?k, i.e.,
2k?>?k2?? (1)
Now, we have to prove that P(k? 1) is true whenever P(k) is true, i.e. we have to prove that 2k? 1?> (k? 1)2.
From equation (1), we obtain
2k?>?k2
On multiplying both sides with 2, we obtain
2 ? 2k?> 2 ??k2
2k? 1?> 2k2
?To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2.
Let us assume 2k2?> (k? 1)2.
? 2k2?>?k2? 2k? 1
??k2?> 2k? 1
??k2?? 2k?? 1 > 0
? (k?? 1)2?? 2 > 0
? (k?? 1)2?> 2, which is true as?k?> 4
Hence, our assumption 2k2?> (k? 1)2?is correct and we have 2k? 1?> (k? 1)2.
Thus, P(n) is true for?n?=?k? 1.
Thus, by the principle of mathematical induction, the given mathematical statement is true for every positive integer?n.
?
IN THIS EXAMPLE IT HAS BEEN WRITTEN THAT ,
To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2.
how?2k? 1?> (k? 1)2?=?2k2?> (k? 1)2
I cant understand how so plz explain that
Answer
1
Nura Mohammad
Subject: Maths
, asked on 25/11/17
How is the underlined step coming??
Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz expain how to solve dis...
25
.
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S
1
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3
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1
)
322
2
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324
3
)
325
4
)
326
Answer
2
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz expain how to solve dis...:
23. If S
1
={2}, S
2
={3,6}, S
3
={4,8,16}, S
4
={5,10,20,40},..... then the sum of numbers in the set S
15
is .
1) 5(2
15
) 2) 16(2
15
-1)
3) 16 (2
16
-1) 4) 15(5
15
-1)
Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
P
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2
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Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz explain how to solve dis...
Q.19.
1
2
tan
x
2
+
1
4
tan
x
4
+
.
.
.
+
1
2
n
tan
x
2
n
=
Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz expain how to solve dis...
Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
P
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+
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Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Q
.
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Answer
1
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz explain how to solve dis...
Q.3.
∑
k
=
1
n
k
1
+
1
n
k
-
1
=
Answer
2
Chharishma.r.nayaka
Subject: Maths
, asked on 27/10/17
Plz explain how to solve dis...
1) n (n - 1)
2) n (n + 1)
3)
n
2
4)
n
+
1
2
Answer
1
Prev
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Next
What are you looking for?
Please explain the last line of solution
2n?>?n2, where?n?is a positive integer such that?n?> 4.
Solution:
Let the given statement be P(n), i.e.,
P(n) : 2n?>?n2?where?n?> 4
For?n?= 5,
25?= 32 and 52?= 25
?25?> 52
Thus, P(n) is true for?n?= 5.
Let P(n) be true for?n?=?k, i.e.,
2k?>?k2?? (1)
Now, we have to prove that P(k? 1) is true whenever P(k) is true, i.e. we have to prove that 2k? 1?> (k? 1)2.
From equation (1), we obtain
2k?>?k2
On multiplying both sides with 2, we obtain
2 ? 2k?> 2 ??k2
2k? 1?> 2k2
?To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2.
Let us assume 2k2?> (k? 1)2.
? 2k2?>?k2? 2k? 1
??k2?> 2k? 1
??k2?? 2k?? 1 > 0
? (k?? 1)2?? 2 > 0
? (k?? 1)2?> 2, which is true as?k?> 4
Hence, our assumption 2k2?> (k? 1)2?is correct and we have 2k? 1?> (k? 1)2.
Thus, P(n) is true for?n?=?k? 1.
Thus, by the principle of mathematical induction, the given mathematical statement is true for every positive integer?n.
?
IN THIS EXAMPLE IT HAS BEEN WRITTEN THAT ,
To prove 2k? 1?> (k? 1)2, we only need to prove that 2k2?> (k? 1)2.
how?2k? 1?> (k? 1)2?=?2k2?> (k? 1)2
I cant understand how so plz explain that
23. If S1={2}, S2={3,6}, S3={4,8,16}, S4={5,10,20,40},..... then the sum of numbers in the set S15 is .
1) 5(215) 2) 16(215-1)
3) 16 (216-1) 4) 15(515-1)
Q.19.
Q.3.
1) n (n - 1)
2) n (n + 1)
3)
4)