If p(n) is the statement (n)2 100, prove that p(r+1) is true whenever p(r) is true - Maths - Principle of Mathematical Induction

Question

If p(n) is the statement (n)2>100, prove that p(r+1) is true
whenever p(r) is true

Aarushi Mishra · Accepted Answer

Let Pr be truePr: r2>100Pr+1:r+12>100L H
S
r+12=r2+2r+1Since r is antural number sor+12=r2+2r+1>r2r+12>r2Using Prr+12>r2>100r+12>100Hence Pr+1 is true if Pr is true

If p(n) is the statement (n)2>100, prove that p(r+1) is true whenever p(r) is true