Question

Sum of last 30 coefficients in the binomial expansion of \( (1+x)^{59} \) is

• A. \( 2^{29} \)
• B. \( 2^{59} \)
• C. \( 2^{58} \)
• D. \( 2^{59} - 2^{29} \)
• E. \( 2^{60} \)

Hint:

Use symmetry of binomial coefficients to split sums efficiently.

Answer 1

The Correct Option is D

Concept: Sum of all coefficients: \[ (1+1)^{59} = 2^{59} \]

Step 1: Total terms = 60.
Last 30 terms correspond to second half.

Step 2: Use symmetry.
Sum of first 30 = \( 2^{58} \)

Step 3: Subtract.
\[ \text{Last 30} = 2^{59} - 2^{29} \]