Call me

Have a Query? We will call you right away.

+91

E.g: 9876543210, 01112345678

We will give you a call shortly, Thank You

Office hours: 9:00 am to 9:00 pm IST (7 days a week)

What are you looking for?

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 9^{2n}+ 2^{3n-3}, 3^{n-1}is divisible by 25, for all n Ꜫ N.Please 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?

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 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

using principle of mathematical induction prove that, 1

^{2}+ 2^{2}+....+ n^{2}(n^{3}/3) for all n belonging to natural numbers= 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.

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

P.T by principle of mathematical induction

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

^{n-1}= 5/2(3^{n-1})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.?(1) 2ac = ab + bc (2) 2ab = ac + bc (3) 2b = a + c (4) b

^{2}= ac3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)

Q. Prove by the method of induction, that ${1}_{n}=10-{\left(5+\sqrt{17}\right)}^{n}-{\left(5-\sqrt{17}\right)}^{n}isdivisibleby{2}^{n+1}$

for all n>1.

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 nENQ. Using the principle of mathematical induction, prove that n

^{5}/5 + n^{3}/3 + 7^{n}/15 is a natural number~~V~~nEN.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+3+3

^{2}+.....+3^{n-1}={3^{n-1}-1}2prove the following with the help of principle of mathematical induction

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

1n(3n-1)2

How does (k+2)(k+1) become P(k+1) in the video?

Prove by PMI

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

Prove 2220

^{2n}^{+1}+2003^{2n+1}is divisible by 4005,nbelongs toNin 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.in 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).11 power n+2 + 12 power 2n+1 is divisible by 133

(1+2+3+.+n)

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}).n(n+1)(n+2) is a multiple of 6

can anyone tell me how to solve (k+1){1/3k(4k+11)+2(2k+5)}

i dont understand why the next step is 1/3(k+1) {4k

^{2}+23k + 30}Prove by induction that (2n+7)<(n+3)

^{2}is true7 divides 2

^{3n}-1^{2}-1) is divisible by 24 where n is an odd number greater than 2.using mathematical induction prove that

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

7

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

Prove by Principle of Mathematical Induction:

12

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