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Syllabus

sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)

1^4+2^4+3^4+..........+n^4 =n(n+1)(2n+1)+(3n^2+3n-1)/30. (whole divided by 30)

Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)

2^5n>3^3n for n belongs to natural no.

sinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx

prove by PMI

5+15+45....+5.3

^{n-1}= 5/2(3^{n-1})prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .

Prove that 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]

Prove that x

^{2n}-y^{2n}is divisible by x+y?solve this equation :-

4k

^{3}+ 18k^{2}+ 23k + 9 =0 (step by step)Prove that n(n+1)(n+5) is a multiple of 3

Prove by PMI

1) a+(a+d)+(a+2d)+ ......[a+(n-1)d] = n/2 [2a+(n-1)d], n E N.

2) n(n+1)(n+5) is divisible by 6 for all n E N.

3) 9 raised to n - 8n - 1 is a multiple of 64 for all n E N.

Prove that n(n+1)(n+2) is divisible by 6

Using PMI Prove that 1^2 + 2^2 + ......... + n^2 n^3/3

1.2 + 2.2

^{2}+ 3.2^{2}+ … +n.2^{n}= (n– 1) 2^{n}^{+1}+ 2this question is solved on this site...... but I can't understand how the final answer came ..... please see 4.1's 8th question on this site ......

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9Please help me I can't solve questions of mathematical induction.I tried a lot but I always get confused in the (k+1)th step.Please tell what to do?

^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1

Prove that 11

^{n+2 }+ 12^{2n+1 }is divisible by 133 for all n belongs to N .= 9

^{(}^{k}^{ + 1) }(8 + 1)= 8. 9

^{(}^{k}^{ + 1)}+ 9^{(}^{k}^{ + 1)}can anyone explain me 2 step how it came...please it is of example no 1.

Prove: 5

^{2n}-1 is divisible by 24 for all n NUsing PMI, prove that

5

^{2n+2}-24n-25 is divisible by 576 for n belongs to N.Prove the following

1.3 + 3.5 + 5.7 + ..... +(2n - 1) (2n + 1 ) =n( 4n square + 6n -1)/2 plz explain briefly in a simple method

p(n) =1+4+7+...+(3n-2)=1/2n(3n-1)

P.T by principle of mathematical induction

using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbersQ. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),

~~V~~nEN.how to split a cubic polynomial like k

^{3}+6k^{2}+9k+4??bY PMI prove n(n+1)(2n+1) is divisible by 6

5+15+45+....+5.3

^{n-1}= 5/2(3^{n-1})Prove that 2.7

^{n}+ 3.5^{n}-5 is divisible by 24, for all n belongs to N....Plzzz dnt tell to refer textbook as frm dat also its not clear to me plzzzzzz answer it as soon as possible.....Prove by induction:

1/1.2 + 1/2.3 + 1/3.4 + ..... to n terms = n/(n+1)

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.using mathematical induction

prove that

7+ 77+ 777+ ..............+ 77.........7 = 7/81 (10to the power n+1 -9n-10)

1 / 1.2.3 + 1 / 2.3.4 + 1 / 3.4.5 + …….. + 1 / n (n+1) (n+2) = n (n+3) / 4 (n+1) (n+2) ? using principle of mathematical induction prove the following for all n E N ?

Prove that n

^{2}+ n is even , where n is natural number.?prove dt ....

3

^{4n+2}+ 5^{2n+1 is a multiple of 14}3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

What is actually the meaning of "MATHEMATICAL INDUCTION" what are the principles involved in it?????........

plz ans fast!!!!!!!:)

Find all positive integers n such that 3

^{2n}+ 3n^{2}+ 7 is a perfect square.1/2*5+ 1/5*8 + 1/8*11 +.......................+

1/(3n-1)(3n+2)

= n/6n+4

prove by PMI

Suppose there is a given statement P(n) involving the natural numbernsuch thatThe statement is true forn= 1, i.e., P(1) is true

What "P" MEANS and How P(1) IS true??????????Please explain I don't got it frm study material.............prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENin ncert example 2 step 5 its given:

2

^{k+1 }˃ 2k = k+k > k+1how is 2^{k+1 }˃ k+1? explain stepwise and in detail.(expert only).(1+2+3+.+n)

Hi

By using principle of mathematical induction, prove that for all n element of N:

3^2n+2 - 8n - 9 is divisible by 64.

1/1.2 + 1/2.3 = 1/3.4 +.........+ 1/n(n+1 )= n/n+1 using principle of mathematical induction

1+4+7+---------+(3n-2)=

1n(3n-1)2

^{th}term is a+(n-1)d, Prove it by Mathematical Induction?^{n }> or = 2^{n}by Principle of Mathematical Induction.Prove by PMI

n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers

By Principle of Mathematical Induction, prove that:

12

^{n}+ 2.5^{n-1}is divisible by 7.

in drilling worlds deepest hole it was found that the temperature T in degree celcius at x km below the surface of the earth was =30+25(x - 3), 3 less than x less than 15. at what depth will the temperature lie b/w 200

^{o}C and 300^{o}C.11 power n+2 + 12 power 2n+1 is divisible by 133

1. two classes meet at the same hr.

2. two classes meet at different hrs. and 30 students are enrolled in both the courses

3. what value is shown here?

Prove that

^{ 1}/_{2 }tan (^{x}/_{2})+^{1}/_{4}tan(^{x}/_{4})+...+(^{1}/_{2n})tan (^{x}/_{2n})=(^{1}/_{2n})cot(^{x}/_{2}^{n}) - cotx for all n (- N and 0<x<(^{pi}/_{2}).2.7

^{n}+3.5^{n}-5 is divided b 24, for all n$\in $N1 sq+2sq+3sq+4sq+......+n sq =n(n+1)(2n+1)/6.

please do the calculations in simplest way with details and please no links

Prove by induction that (2n+7)<(n+3)

^{2}is truepls someone explain how to prove the problems in this chapter ! its so confusing especially the last 3-4 steps ! :(( !

rnrevision notes or tips ..... pls reply

7 divides 2

^{3n}-1what is this principle of mathematic induction used for?

using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.What is the difference between mathematical deduction and induction?

what is principle of mathamatical induction

Prove that (2n)! /2

^{2n}(n!)^{2}<=1/in root whole 3n +1 for all n belonging to natural numbers by PMI.7

^{n}-3^{n}is a divisible by 4.please solve this

In Example 3,from where did 2(k+1){2(k+1)+3} in the first line of to prove P(K+1).

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Prove the following by using the principle of mathematical induction for all

(2

n+7) < (n+ 3)^{2 }can any pls explain this question in detail??? cuz i can't get it

1. 2.7

^{n}+ 3.5^{n}-5 is divisible by 24,n belongs to natural number2. 3

^{2n-2}-8n-9 is divisible by 8 ,n belongs to natural numberprove that 2

^{n}is greater than n for all positive integers n.this is example 2 from the ncert maths text book.

plzz...answer soon....i dint get the last step.

using PMI prove that 3 to the power (2n-1) is divisible by 8 where n belongs to N.

plz reply