If the number of terms in the expansion of 1 + x 101 1 + x 2 - x 100 is n , then the value of n 25 is equal to

Question

If the number of terms in the expansion of 1 + x 101 1 + x 2 - x 100 is n , then the value of n 25 is equal to,

MARKS App · Accepted Answer

1 + x 101 1 + x 2 - x 100 = 1 + x 1 + x 1 - x + x 2 100 = 1 + x 1 + x 3 100 = 1 × 1 + x 3 100 + x × 1 + x 3 100 So, the number of terms = ( 101 terms of the form x 3 k ) + ( 101 terms of the form x 3 k + 1 ) = 202 terms ⇒ n = 202

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