00:01
Hi, in this question we have to prove mathematical induction.
00:07
1 square plus 2 square plus 3 square plus etc up to n square equals n into n plus 1 into 2 n plus 1 divided by 6.
00:21
Here let this as p of n.
00:26
First we have to prove for n equals 1.
00:30
So, here lhs equals 1 square which is equal to 1 and rhs equals 1 into 1 plus 1 into 2 into 1 is 2 plus 1 divided by 6 which is equal to 1 into 2 into 3 divided by 6 which is equal to 1.
00:51
Hence conclude that rhs equals lhs.
00:57
So, that p of n is true for n equals 1.
01:05
Next we have to assume that p of k is true.
01:15
So, that we can write it as p of k equals 1 square plus 2 square plus 3 square plus etc plus k square equals k into k plus 1 into 2k plus 1 divided by 6.
01:33
Let this as equation number 1.
01:35
Next we have to prove for p of k plus 1 as true...
