Let's take a look at how product is an instance of a more general function called accumulate, which we would like to implement:

def accumulate$($fuse$,$ start, n$,$ term$)$:

$"""$Return the result of fusing together the first n terms in a sequence

and start. The terms to be fused are term$(1),$ term$(2),...,$ term$($n$).$

The function fuse is a two$-$argument commutative & associative function.

$>>>$ accumulate$($add$,0,5,$ identity$)$ # $0+1+2+3+4+5$

$15$

$>>>$ accumulate$($add$,11,5,$ identity$)$ # $11+1+2+3+4+5$

$26$

$>>>$ accumulate$($add$,11,0,$ identity$)$ # $11($fuse is never used$)$

$11$

$>>>$ accumulate$($add$,11,3,$ square$)$ # $11+1^2+2^2+3^2$

$25$

$>>>$ accumulate$($mul$,2,3,$ square$)$ # $2*1^2*2^2*3^2$

$72$

$>>>$ # $2+(1^2+1)+(2^2+1)+(3^2+1)$

$>>>$ accumulate$($lambda x$,$ y: x $+$ y $+1,2,3,$ square$)$

$19$

$"""$

$"***$ YOUR CODE HERE $***"$

accumulate has the following parameters:

fuse: a two$-$argument function that specifies how the current term is fused with the previously accumulated terms

start: value at which to start the accumulation

n: a non$-$negative integer indicating the number of terms to fuse

term: a single$-$argument function; term$($i$)$ is the ith term of the sequence

Implement accumulate, which fuses the first n terms of the sequence defined by term with the start value using the fuse function.

For example, the result of accumulate$($add$,11,3,$ square$)$ is

add$(11,$ add$($square$(1),$ add$($square$(2),$ square$(3))))=$

$11+$ square$(1)+$ square$(2)+$ square$(3)=$

$11+1+4+9=25$

Assume that fuse is commutative, fuse$($a$,$ b$)==$ fuse$($b$,$ a$),$ and associative, fuse$($fuse$($a$,$ b$),$ c$)==$ fuse$($a$,$ fuse$($b$,$ c$)).$

Then, implement summation $($from lecture$)$ and product as one$-$line calls to accumulate.

Important: Both summation$\_$using$\_$accumulate and product$\_$using$\_$accumulate should be implemented with a single line of code starting with return