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Write the power series for (1 + x)k in terms of binomial coefficients.

Question

Write the power series for 

(1 + x)k

 in terms of binomial coefficients.

check_circleAnswer
Step 1

The binomial theorem is given below:

(a+b)*
=d+ka*\b+ k(k-1) q-2z2 + k(k -1)(k,2) q-3z3 +
+*
2!
3!
k!
k!
-ab
k!
k!
k!
+...
k!
(k-3)! 3!
(k-1)!
(k-2)! 2!
(k-0)! 0!
k
C}
k
k
k
a-2b2 +
a*-3b3 +.
k
2
3
help_outline

Image Transcriptionclose

(a+b)* =d+ka*\b+ k(k-1) q-2z2 + k(k -1)(k,2) q-3z3 + +* 2! 3! k! k! -ab k! k! k! +... k! (k-3)! 3! (k-1)! (k-2)! 2! (k-0)! 0! k C} k k k a-2b2 + a*-3b3 +. k 2 3

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Step 2

We need to write the power series for (1 + x)k   in terms of...

k
k
k
(1x)
14
k-1
1-212
2
|k-3 3
+
0
1
3
k
help_outline

Image Transcriptionclose

k k k (1x) 14 k-1 1-212 2 |k-3 3 + 0 1 3 k

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Math

Calculus

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