Question

Use mathematical induction to prove that statement,1²+2²+3³+.....+n²=n(n+1)(2n+1)/6

Answer 1

Answer:

Rest of all u can solve by urself.......

Hope this will help u.....

Answer 2

Step-by-step explanation:

in 1st case n=1

n(n+1)(2n+1)/6=n^2

1(1+1)(2*1+1)/6=1^2

1(2)(3)/6=1

6/6=1

1=1

LHS=RHS

in 2nd case n=k

1^2+2^2+3^3+........+n^2=(n+1)(2n+1)/6

1^2+2^2+3^3+........+k^2=(k+1)(2k+1)/6

=2k^2+3k+1/6....eq1

in 3rd case n=k+1

1^2+2^2+3^3+........+k+1^2=(k+1+1) (2(k+1)+1)/6

1^2+2^2+3^3+........+k+1^2=(k+2)(2k+3)/6...eq2

substitute

2k^2+3k+1/6+(k+1)^2=3k^2+7k+6/6

2k^2+3k+1+(6k+6)^2=3k^2+7k+6