Question

How to the turn 2x^3+4x^5+8x^7+16x^9+32x^11+64x^13 into sigma notation

Answer 1

Explanation:

Given:

total number of terms (n) = 6

sequence of the coefficients

= 2, 4, 8, 16, 32, 64

= 2¹, 2², 2³, 2⁴, 2⁵ → 2ⁿ

sequence of the power of x

= 3, 5, 7, 9, 11, 13

= 2(1)+1, 2(2)+1, 2(3)+1, 2(4)+1, 2(5)+1, 2(6)+1 → 2n+1

Therefore the formula =
`2^nx^(2n+1)`

`\boxed{\sum_(n=1)^(total\ terms)(formula)}`

`\sum_(n=1)^(6)(2^nx^(2n+1))`