Use mathematical induction to prove the statement is true fo

Use mathematical induction to prove the statement is true for all possible integers n.

10 + 30 + 60 + ... + 10n = 5n(n+1)

Solution

given statement 10 + 30 + 60 + ... + 10n = 5n(n+1)

for n =1

=>10=5*1*(1+1)

=>10=10 ,true

let us assume that statement is true for n =k

=>10 + 30 + 60 + ... + 10k = 5k(k+1)

now for n =k+1

10 + 30 + 60 + ... + 10k+10(k+1)

=[10 + 30 + 60 + ... + 10k]+[10(k+1)]

=[5k(k+1)]+ [10(k+1)]

=[5k(k+1)]+ [5*2*(k+1)]

=5(k+1)[k+2]

=5(k+1)((k+1)+1)

so n=k+1 satisfies the given statement

so by mathematical induction the statement is true for all possible integers n