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Chaitanya Sharma
Subject: Maths
, asked on 27/2/17
Please solve this all question
Fast
Answer
4
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/2/17
If
n
belongs to
natural number,
then by
PMI
prove that,
n.1 + (n-1).2 + (n-2).3 + ... + 2.(n-1) + 1.n = n(n+1)(n+2)/6
NO
LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/2/17
If
n
belong
to
Natural numbers,
then by
PMI prove
that,
(i) 1 + 2 + 3 + g + n < (2n + 1)
^{2}
/8
(ii) 1
^{2}
+ 2
^{2}
+3
^{2}
+ g + n
^{2}
> n
^{3}
/3
NO LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 9/2/17
For what natural number
n
the inequality
2
^{n}
> 2n+1
is valid.
[Answer :
n is greater than equal to 3
]
NO LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 31/1/17
If
n belongs to N
, then by
PMI
prove that,
(a) n < 2n
(b) 3n > n
^{3 }
[n>=4]
(c) 2
^{n }
< n! [n>=4]
(d)3
^{n }
> 2
^{n}
All the above four sub-questions are included in a single question.
Please do not consider them as different questions.
NO LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 30/1/17
If
1.1 ! + 2.2 ! + 3..3 ! +...+n.n ! = (n+1) ! -1
, then show by
PMI
that,
1.1 ! + 2.2 ! + 3.3 ! + ...+ n.n ! + (n+1)(n+1) ! = (n+2) ! -1
NO LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 30/1/17
If for all n belongs N
2n+7< (n+3)
^{2}
then show that,
2(n+1)+7<(n+4)
^{2}
NO LINKS PLEASE
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 30/1/17
For all
n belongs to N
, prove by
principle of mathematical
induction
that,
(cos
ɵ
+
i
sin
ɵ
) = cos
nɵ
+
i
sin
nɵ
Answer
1
Shubhrajyoti Ghosh
Subject: Maths
, asked on 30/1/17
For all n
belongs
to
N
, prove by principle of mathematical induction,
2
^{2}
+5
^{2}
+8
^{2}
...to n terms = n/2(6n
^{2}
+3n-1)
NO LINKS PLEASE
Answer
1
Poonam Tripathi
Subject: Maths
, asked on 13/12/16
urgnt
Answer
2
Amaatye Mahajan
Subject: Maths
, asked on 4/12/16
Using principle of mathematical induction show that cosα + cos(α+β) + cos(α+2β)+… + cos(α+(n-1) β) = cos{α+(n-1/2) β}sin(nβ/2)/sinβ/2
Answer
1
Srishti
Subject: Maths
, asked on 5/11/16
Please explain the underlined steps. How can we take 7 in common?
Answer
1
Archita Srivastava
Subject: Maths
, asked on 1/11/16
solve
Answer
1
A. Nethra Krupa
Subject: Maths
, asked on 27/10/16
By using PMI prove the binomial theorem expansion {i.e (a+b)
^{n }
= a
^{n}
+nc
_{1}
a
^{n-1 }
+nc
_{2}
a
^{n-2}
b+ .....+ nc
_{r}
a
^{n-r}
b
^{r }
+.....}
Answer
2
Shruti Sinha
Subject: Maths
, asked on 13/10/16
By the Principle of Mathematical Induction show that 10
^{n}
+ 3.4
^{n+2}
+ k is divisible by 9 for all n € N. (Note that 3.4 is not a decimal, but a product) Thank you experts, and please don’t give any links if it can be helped.
Answer
1
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nbelongs tonatural number,then byPMIprove that,n.1 + (n-1).2 + (n-2).3 + ... + 2.(n-1) + 1.n = n(n+1)(n+2)/6NOLINKS PLEASEnbelongNatural numbers,then byPMI provethat,(i) 1 + 2 + 3 + g + n < (2n + 1)

^{2}/8(ii) 1

^{2}+ 2^{2}+3^{2}+ g + n^{2}> n^{3}/3NO LINKS PLEASEnthe inequality2is valid.^{n}> 2n+1[Answer :

]n is greater than equal to 3NO LINKS PLEASE, then byn belongs to Nprove that,PMI(a) n < 2n(b) 3n > n

^{3 }[n>=4](c) 2

^{n }< n! [n>=4](d)3

^{n }> 2^{n}All the above four sub-questions are included in a single question.

Please do not consider them as different questions.NO LINKS PLEASE, then show by1.1 ! + 2.2 ! + 3..3 ! +...+n.n ! = (n+1) ! -1PMIthat,1.1 ! + 2.2 ! + 3.3 ! + ...+ n.n ! + (n+1)(n+1) ! = (n+2) ! -1NO LINKS PLEASE

then show that,2n+7< (n+3)^{2}2(n+1)+7<(n+4)^{2}NO LINKS PLEASE

n belongs to N, prove byprinciple of mathematicalinductionthat,(cos

ɵ+isinɵ) = cosnɵ+isinnɵbelongstoN, prove by principle of mathematical induction,2^{2}+5^{2}+8^{2}...to n terms = n/2(6n^{2}+3n-1)NO LINKS PLEASE

solve

^{n }= a^{n}+nc_{1}a^{n-1 }+nc_{2}a^{n-2}b+ .....+ nc_{r}a^{n-r}b^{r }+.....}^{n}+ 3.4^{n+2}+ k is divisible by 9 for all n € N. (Note that 3.4 is not a decimal, but a product) Thank you experts, and please don’t give any links if it can be helped.