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=n³+3n²+5n+3 is divisible by 3 for all 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+4+7+---------+(3n-2)=1 n(3n-1) 

                                         2

Prove 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^oC and 300^oC.

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).

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

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

7 divides 2³ⁿ-1

using mathematical induction prove that n(n+1)(n+2) is divisible by 6.