Investigation on Binomial Theorem

SamarpanRai 10/1/12 MrYadavPanta Mathematical Investigation on binomial Theorem In the enlargement of (a+b)2we date, = (a+b) (a+b) =a(a+b)+b(a+b) =a2+ab+ab+b2 =a2+2ab+b2 In the intricacy of (a+b)3we see, = (a+b) (a+b) (a+b) =(a+b)2 (a+b) =(a2+ab+ab+b2) (a+b) =a (a2+2ab+b2) +b (a2+2ab+b2) = a3+2a2b+ab2+a2b+2ab2+b3 = a3+3a2b+3ab2+b3 In the Expansion of (a+b)4we see, = (a+b) (a+b) (a+b) (a+b) = (a+b)3(a+b) = (a3+3a2b+3ab2+b3) (a+b) = a (a3+3a2b+3ab2+b3) +b (a3+3a2b+3ab2+b3) = a4+3a3b+3a2b2+ab3+a3b+3a2b2+3ab3+b4 =a4+4a3b+6a2b2+4ab3+b4 In the Expansion of (a+b)5 we see, = (a+b) (a+b) (a+b) (a+b) (a+b) = (a+b)4(a+b) = (a4+4a3b+6a2b2+4ab3+b4) (a+b) = a (a4+4a3b+6a2b2+4ab3+b4) +b (a4+4a3b+6a2b2+4ab3+b4) = a5+4a4b+6a3b2+4a2b3+ab4+ a4b+4a3b2+6a2b3+4ab4+b5 = a5+5a4b+10a3b2+10a2b3+5ab4+b5 In the Expansion of (a+b)6 we see, = (a+b) (a+b) (a+b) (a+b) (a+b) (a+b) = (a+b)5 (a+b) = a (a5+5a4b+10a3b2+10a2b3+5ab4+b5) +b (a5+5a4b+10a3b2+10a2b3+5ab4+b5) = a6 +5a5b+10a4b2+10a3b3+5a2b4+ab5+a5b+5a4b2+ 10a3b3+10a2b4+5ab5+b6 =a6 +6a5b+15a4b2+20a3b3+15a2b4+6ab5+b6 observing the higher up mental synthesis we stinkpot put in the smell in the mogul of a and rise up the cost in the expansion. 1. (a+b)2 =a2b0+2ab+a0b2 There ar 3 terms in the expansion 2. (a+b)3 =a3b0+3a2b+3ab2+a0b3 There are 4 terms in the expansion 3.

(a+b)4 =a4b0+4a3b1+6a2b2+4a1b3+a0b4 There are 5 terms in the expansion 4. (a+b)5= a5b0+5a4b+10a3b2+10a2b3+5a1b4+a0b5 There are 6 terms in the expansion 5. (a+b)6 =a6b0 +6a5b+15a4b2+20a3b3+15a2b4+6a1b5+a0b6 There are 7 terms in the expansion flavour at the expressio n terms we find a sexual congress between (! a+b)nand the number of expression. We see the pattern that the number of expression is one greater than n. So, we can predict that the number of expression in (a+b)nis n+1 when n ? 0 In the only in all the terms thus expanded from (a+b)n, the sum of power of separately term is always equals to n. Mathematically, If axby is one of the term then, x+y=n Again, we can see that the...If you want to get a beneficial essay, order it on our website: OrderCustomPaper.com

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