The-number-of-terms-in-the-expansion-of-1-5-2-x-9-1-5-2-x-9-is-

Question Number 12841 by CheaV last updated on 04/May/17

The number of terms in the expansion of

{(1 + 5 \sqrt{2} x)}^{9} + {(1 - 5 \sqrt{2} x)}^{9} is

Answered by malwaan last updated on 04/May/17

5 terms

Answered by mrW1 last updated on 04/May/17

{(a + b)}^{n} + {(a - b)}^{n}

= \underset{k = 0}{\sum^{n}} C_{k}^{n} a^{n - k} b^{k} + \underset{k = 0}{\sum^{n}} C_{k}^{n} a^{n - k} {(- b)}^{k}

= \underset{k = 0}{\sum^{n}} [1 + {(- 1)}^{k}] C_{k}^{n} a^{n - k} b^{k}

= \underset{k = 0}{\sum^{n}} α^{k} C_{k}^{n} a^{k} b^{n - k}

w i t h α^{k} = 1 + {(- 1)}^{k}

f o r n = 9 :

α^{k} = 2 i f k = 0, 2, 4, 6, 8 \Rightarrow 5 t e r m s \neq 0

α^{k} = 0 i f k = 1, 3, 5, 7, 9 \Rightarrow 5 t e r m s = 0

\Rightarrow A n s w e r i s 5 t e r m s

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