Use Mathematical Induction to Prove the Following for Every Positive $n$

question 87

Essay

Use mathematical induction to prove the following for every positive integer $n$ .
$\sum _ { i = 1 } ^ { n } 96 i ^ { 5 } = 8 n ^ { 2 } ( n + 1 ) ^ { 2 } \left( 2 n ^ { 2 } + 2 n - 1 \right)$

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Definitions:

Innominate Bone

Another term for the hip bone, comprising the ilium, ischium, and pubis, which are fused in adults.

Pelvic Girdle

The Pelvic Girdle is a ring-like bony structure, located at the base of the spine, to which the lower limbs are attached in humans and other vertebrates.

Hip Bones

The large bones that form the base of the pelvis and articulate with the femur at the hip joints; these are comprised of three parts: ilium, ischium, and pubis.

Coccyx

The small, triangular bone at the base of the spinal column, consisting of three to five fused vertebrae, also known as the tailbone.