Write the sum of the series : 12 – 22 + 32 – 42 + 52 – 62 + ……. + (2n – 1)2 – (2n)2
S=12 + 32 + 52 ……… + (2n – 1)2 – {22 + 42 + 62 + ……. + (2n)2}
S=12 + 32 + 52 ……… + (2n – 1)2 – 22{12 + 22 + 32 + ……. + (n)2} ……..(1)
We know
………(2)
…(3)
Substituting (3) in (1), we get,
Substituting (2) in the above equation