Q2 of 60 Page 21

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




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