f(n)=f(n-1)+n

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Solution for f(n)=f(n-1)+n equation:


Simplifying
f(n) = f(n + -1) + n

Multiply f * n
fn = f(n + -1) + n

Reorder the terms:
fn = f(-1 + n) + n
fn = (-1 * f + n * f) + n
fn = (-1f + fn) + n

Add '-1fn' to each side of the equation.
fn + -1fn = -1f + fn + -1fn + n

Combine like terms: fn + -1fn = 0
0 = -1f + fn + -1fn + n

Combine like terms: fn + -1fn = 0
0 = -1f + 0 + n
0 = -1f + n

Solving
0 = -1f + n

Solving for variable 'f'.

Move all terms containing f to the left, all other terms to the right.

Add 'f' to each side of the equation.
0 + f = -1f + f + n
Remove the zero:
f = -1f + f + n

Combine like terms: -1f + f = 0
f = 0 + n
f = n

Simplifying
f = n

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