Evaluate :


To find: Value of


Formula used: (I)


(ii) (a+b)n =   nC0an + nC1an-1b + nC2an-2b2 + …… +nCn-1abn-1 + nCnbn


(a+1)5 = 5C0a5 + 5C1a5-11 + 5C2a5-212 + 5C3a5-313 + 5C4a5-414 + 5C515


⇒ 5C0a5 + 5C1a4 + 5C2a3 + 5C3a2 + 5C4a + 5C5… (i)


(a-1)5


⇒ 5C0a5 - 5C1a4 + 5C2a3 - 5C3a2 + 5C4a - 5C5 … (ii)


Substracting (ii) from (i)


(a+1)5 - (a-1)5 = [5C0a5 + 5C1a4 + 5C2a3 + 5C3a2 + 5C4a + 5C5] - [5C0a5 - 5C1a4 + 5C2a3 - 5C3a2 + 5C4a - 5C5]


⇒ 2[5C1a4 + 5C3a2 + 5C5]


⇒ 2


⇒ 2[(5)a4 + (10)a2 + (1)]


⇒ 2[5a4 + 10a2 + 1] = (a+1)5 - (a-1)5


Putting the value of a = in the above equation


= 2[54 + 102 + 1]


⇒ 2[(5)(9) + (10)(3) + 1]


⇒ 2[45+30+1]


⇒ 152


Ans) 152


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