The value of - C 1 15 + 2 · C 2 15 - 3 · 15 C 3 + . . . . . - 15 · C 15 15 + C 1 14 + C 3 14 + C 5 14 + . . . . + C 11 14 is equal to

Question

The value of - C 1 15 + 2 &#183; C 2 15 - 3 &#183; 15 C 3 + . . . . . - 15 &#183; C 15 15 + C 1 14 + C 3 14 + C 5 14 + . . . . + C 11 14 is equal to

Aicharya · Accepted Answer

- C 1 15 + 2 &#183; C 2 15 - 3 &#183; C 3 15 + &#8230; - 15 &#183; C 15 15 + C 1 14 + C 3 14 + &#8230; + C 11 14 = &#8721; r = 1 15 - 1 r &#183; r &#183; 15 C r + C 1 14 + C 3 14 + &#8230; + C 11 14 + C 13 14 - C 13 14 = &#8721; r = 1 15 - 1 r &#183; 15 &#183; C r - 1 14 + 2 13 - 14 = 15 - C 0 14 + C 1 14 &#8230; &#8230; . . - C 14 14 + 2 13 - 14 = 2 13 - 14

The value of - C 1 15 + 2 · C 2 15 - 3 · 15 C 3 + . . . . . - 15 · C 15 15 + C 1 14 + C 3 14…

Solution

The value of - C 1 15 + 2 &#183; C 2 15 - 3 &#183; 15 C 3 + . . . . . - 15 &#183; C 15 15 + C 1 14 + C 3 14…

Solution

The value of - C 1 15 + 2 · C 2 15 - 3 · 15 C 3 + . . . . . - 15 · C 15 15 + C 1 14 + C 3 14…