Ravi
Last Activity: 9 Years ago
Check for n=1...(True)
Let it be true for n=k
i.e.
12+32+52….+(2k-1)2= k(4k2-1)/3 ...(i)
To prove: It is true for n=k+1
Soln.
12+32+52….+[2(k+1)-1]2
= k(4k2-1)/3+ [2k+1]2 ...(from i)
= k(2k+1)(2k-1)/3+ (2k+1)2
=(2k+1)[k(2k-1)/3-(2k+1)]
=(2k+1)(2k+3)(k+1)/3
=(k+1)[2(k+1)+1][2(k+1)-1]/3
=(k+1)[4(k+1)2-1]/3