Question

S=2.4.6+4.6.8+........+98.100.102

Answer 1

S = 2.4.6 + 4.6.8 + ... + 98.100.102

=> 8S = 2.4.6.8 + 4.6.8.8 + ... + 98.100.102.8

=> 8S = 2.4.6.(8 - 0) + 4.6.8.(10 - 2) + ... + 98.100.102.(104 - 96)

=> 8S = 2.4.6.8 - 0 + 4.6.8.10 - 2.4.6.8 + ... + 98.100.102.104 - 96.98.100.102

=> 8S = 98.100.102.104

=> S = 98.100.102.104/8

=> S = 12994800

Answer 2

=> 8S = 2.4.6.8 + 4.6.8.8 + 6.8.10.8 + .... + 98.100.102.8

=> 8S = 2.4.6.8 + 4.6.8.( 10 - 2 ) + 6.8.10.( 12 - 4 ) + .... + 98.100.102.( 104 - 96 )

=> 8S = 2.4.6.8 + 4.6.8.10 - 2.4.6.8 + 6.8.10.12 - 4.6.8.10 + .... + 98.100.102.104 - 96.98.100.102

=> 8S = ( 2.4.6.8 - 2.4.6.8 ) + ( 4.6.8.10 - 4.6.8.10 ) + .... + ( 96.98.100.102 - 96.98.100.102 ) + 98.100.102.104

=> 8S = 98.100.102.104

=> S = \(\frac{98.100.102.104}{8}\)