Page 260 - aljaber
P. 260
RTW@ @pþÝn¾aì@pbÉibnn¾a
2k + 1
( )S2k+1 2 + (2k)× 1
= 2 k2 +1
= 2k + 1 ( 2k 2 + 2k + 2)
2
= (2k + 1)(k2 + k + 1)
= 2k 3 + 3k2 + 3k + 1
= k 3 + 3k 2 + 3k + 1 + k 3 = (k + 1)3 + k 3
:( ) ()
S3n − S2n − Sn
= 3n (2a + (3n − 1)d ) − 2n (2a + (2n − 1)d )
22
−n (2a + (n − 1)d )
2
= n 6a + 9nd − 3d − 4a − 4nd + 2d − 2a − nd + d
2
= n 4nd = 2n2d
2