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sinx+sin2x+sin3x+...+sin nx=sin((n+1)/2)x .((sin nx)/2) / sin(x/2)
7 + 77 + 777 + ....+ 777...(n digits)...7 = 7/81 (10^(n+1) - 9n - 10)
Prove by mathematical induction.
Prove that 1.2 + 2.3 + 3.4 +..............n(n+1) = 1/3 n (n+1)(n+2)
Prove that n2 + n is even , where n is natural number.?
sinx + sin3x + ..............+ sin(2n-1)x = sin^2 nx / sinx
prove by PMI
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 2.7n + 3.5n - 5 is divisible by 24 for all n belongs to N. [ please explain with steps]
prove by using PMI that 4 raise to n + 15n - 1 is divisible by 9 .
Prove that x2n-y2n is divisible by x+y?
Prove that n(n+1)(n+5) is a multiple of 3
Prove that n(n+1)(n+2) is divisible by 6
1^4+2^4+3^4+..........+n^4 =n(n+1)(2n+1)+(3n^2+3n-1)/30. (whole divided by 30)
using induction, prove that 10n + 3.4n+2 + 5 is divisible by 9
Using PMI, prove that
52n+2-24n-25 is divisible by 576 for n belongs to N.
Using PMI Prove that 1^2 + 2^2 + ......... + n^2 n^3/3
Prove that 11n+2 + 122n+1 is divisible by 133 for all n belongs to N .
P.T by principle of mathematical induction
find the equation of parabola whose focus is (1,1) and tangent at the vertex is x + y = 1
prove by ibduction that the sum Sn=n3+3n2+5n+3 is divisible by 3 for all nEN
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
Q. Prove that 1.3+2.4+3.5+....+n(n+2) = 1/6n (n+1) (2n+7),V nEN.
Prove that 2.7n + 3.5n-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.....
using principle of mathematical induction prove that, 12 + 22 +....+ n2 (n3/3) for all n belonging to natural numbers
by mathematical induction prove that :
x2n-1 -1 is divisible by x-1
Prove by induction:
1/1.2 + 1/2.3 + 1/3.4 + ..... to n terms = n/(n+1)
how to split a cubic polynomial like k3+6k2+9k+4??
using mathematical induction
7+ 77+ 777+ ..............+ 77.........7 = 7/81 (10to the power n+1 -9n-10)
3.6 +6.9+9.12+....+3n(3n+3) = 3n(n+1) (n+2)
bY PMI prove n(n+1)(2n+1) is divisible by 6
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: 52n-1 is divisible by 24 for all n N
By using principle of mathematical induction, prove that for all n element of N:
3^2n+2 - 8n - 9 is divisible by 64.
1/2*5+ 1/5*8 + 1/8*11 +.......................+
If P(n) is the statement “2n> 3n” and if P(k) is true, show that p(k+1) is also true .
11 power n+2 + 12 power 2n+1 is divisible by 133
Find the multiplicative inverse of (6+5i)2
what is principle of mathamatical induction
Prove , by mathematical induction , that 5n+1+4.6n when divided by 20 leaves remainder 9 for all n
Prove by induction that (2n+7)<(n+3)2is true
7 divides 23n-1
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 200oC and 300oC.
Prove that 1/2 tan (x/2)+1/4tan(x/4)+...+(1/2n)tan (x/2n)=(1/2n)cot(x/2n) - cotx for all n (- N and 0<x<(pi/2).
Using the principle of mathematical induction, prove for n belonging to N:
(2^3n - 1) is divisible by 7
using mathematical induction prove that n(n+1)(n+2) is divisible by 6.
1/1.2 + 1/2.3 = 1/3.4 +.........+ 1/n(n+1 )= n/n+1 using principle of mathematical induction
X+ 4x + 7x + ….. (3n-2)x = 1/2n(3n-1)x .
7n-3n is a divisible by 4.
please solve this
n(n+1)(n+5) is divisible by 6 for all n belongs to natural numbers
Prove the following by using the principle of mathematical induction for all
(2n+7) < (n+ 3)2
can any pls explain this question in detail??? cuz i can't get it
Prove by mathematical induction that n(n+1) (2n+1) is a multiple of 6 for all n∈N
PROVE BY M.I (41)n-(14) is multiple of 27
Prove the following by the PMI :
n7/ 7 + n5 / 5 + n3 / 3 + n2/ 2 - 37/210n is a positive integer for all n belongs to N.
prove that 2n 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.
for every positive integer n.prove that 7n-3n is divisible by 4
prove the following by mathematical induction:- 102N-1+1 IS DIVISIBLE BY 11
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