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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)

1 sqare + 2 square + 3 square +.............+n square >n cube +3 . prove it by mathematical induction.

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

prove by PMI

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]

5+15+45....+5.3

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

^{2n}-y^{2n}is divisible by x+y?for every positive integer n, prove that 7^n- 3^n is divisible by 4 plz expertz explain me how to solve dis step by step

Prove that n(n+1)(n+5) is a multiple of 3

13. Prove that, 5

^{n}- 5 is divisible by 4 for all n $\in $ N.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

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?

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

using induction, prove that 10

^{n }+ 3.4^{n+2}+ 5 is divisible by 9^{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 .Prove: 5

^{2n}-1 is divisible by 24 for all n Nsin theta + sin 2 theta + sin 3 theta + .......+ sin n theta = [sin ( n + 1)/2 / sin 0/2 ] multiplyby sin n theta / sin 0 /2 dont be confused experts this question is related to pmi so clear my doubts by providing the solution of my query of exact question without providing any link.

Using 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

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.1/2x5 + 1/5x8 + 1/8x11 + ....................+ 1/(3n-1)(3n+2) = n / 6n+4

prove by PMI

how to split a cubic polynomial like k

^{3}+6k^{2}+9k+4??Prove by using principle of mathematical induction :cos a+ cos (a+b)+ cos (a+2b)+......+cos [a+(n-1)b] = {cos [a+ ((n-1)/2)b]sin (nb/2)}/sin (b/2)

bY PMI prove n(n+1)(2n+1) is divisible by 6

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)

find the sine of the angle between the vectors a and b if

a = î – 2k; b= ĵ – 4k

where k is k cap

find the angle between the vectors 4 î – 3 ĵ + 3k and 2 î – 3 ĵ + 2k

in quad ABCD prove that AD + BC = 2MN where MN are the midpoints of sides AB and CD respectively.

In triangle ABC , if D, E, F are the midpoints of side BC, CA, AB, respectively

show that

AD +BE +CF = 0

If a = 2 î – k; b= - î + 3k and c = î +2k find scalars x and y such that c = xa + yb

^{5}/5+n^{3}/3+7n/15 is a natural number by using the principle of mathematical induction.^{2}-1) is divisible by 24 where n is an odd number greater than 2.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.?9n - 8n -1 is a multiple of 8

3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

Prove that, x

^{2n}- y^{2n}is divisible by x+y.1/2*5+ 1/5*8 + 1/8*11 +.......................+

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

= n/6n+4

prove by PMI

prove by ibduction that the sum Sn=n

^{3}+3n^{2}+5n+3 is divisible by 3 for all nENHi

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

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

1 + 1/4 + 1/9 + 1/16 +....+ 1/n?

11 power n+2 + 12 power 2n+1 is divisible by 133

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

1n(3n-1)2

^{2n}+ 16n -1 is divisible by 64 Prove by mathematical inductionProve by PMI

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

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.please explain the example no.2 that this is done

To prove 2

^{k}^{ + 1}> (k+ 1)^{2}, we only need to prove that 2k^{2}> (k+ 1)^{2}.Let us assume 2

k^{2}> (k+ 1)^{2}.⇒ 2

k^{2}>k^{2}+ 2k+ 1⇒

k^{2}> 2k+ 1⇒

k^{2}− 2^{k}− 1 > 0⇒ (

k− 1)^{2}− 2 > 0⇒ (

k− 1)^{2}> 2, which is true ask> 4Prove 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}).Prove by induction that (2n+7)<(n+3)

^{2}is true7 divides 2

^{3n}-1prove that 41

^{n}- 14^{n}is a multiple of 27.using mathematical induction prove that

n(n+1)(n+2) is divisible by 6.what is principle of mathamatical induction

Prove that 2.7

^{n}+ 3.5^{n}- 5 is divisible by 24 for all n belongs to N.7

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

PROVE BY M.I (41)

^{n}-(14) is multiple of 27Pls answer fast ...

Prove 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

prove 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.

^{n-1}a) = sin 2^{n}a / 2^{n}sin a