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sum of the given series is: 12+16+24+40+.....

sum of the given series is:
12+16+24+40+.....

Grade:12th pass

1 Answers

Y RAJYALAKSHMI
45 Points
6 years ago
12 + 16 + 24 + 40 …... = (8 + 4) + (8 + 4 * 2) + (8 + 4 * 2^2) + (8 + 4 * 2^3) + ….
= 8 + 8 + 8 + …. n terms + (4 + 4 * 2) + (4 * 2^2) + (4 * 2^3) + …. n terms
8 + 8 + 8 + …. n terms = 8n
(4 + 4 * 2) + (4 * 2^2) + (4 * 2^3) + …. n terms = 4(2^n – 1) /( 2 – 1) = 4(2^n – 1)    
(This is in GP where a =  4 & 4 = 2,  Sn = a( r^n – 1)/(r – 1)
Sun of the given series =  8n + 4(2^n – 1)
 

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