Question

CITIT
) Find (70^ – 69^) + (68^-67^)+(66^–65^) + ...
+(2²-1²) find maths 11th power series in SEQUENCE AND SERIES​

Answer 1

The sum of the given sequence is "2485".

Step-by-step explanation:

The series are

($70^{2}$ - $70^{2}$), ($68^{2}$ - $67^{2}$),

($66^{2}$ - $65^{2}$), ......, ($2^{2}$ - $1^{2}$).

= ( 70 + 69) ( 70 - 69) + ( 68+ 67) ( 68 - 67)  + ( 66 + 65) ( 66 - 65) + .....+ ( 2 + 1) ( 2- 1)

= ( 70 + 69) ·1 + ( 68+ 67) ·1 + ( 66 + 65) ·1+ .....+ ( 2 + 1) .1

= ( 70 + 69) + ( 68+ 67) + ( 66 + 65) + .....+ ( 2 + 1)

= 1 + 2 + 3 + .......+ 70

∴ Sum = $\frac{70(70 + 1)}{2}$  [∵ 1 + 2 + 3 + .......+ n =

$\frac{n(n + 1)}{2}$ ]

= 35 × 71 = 2485

Hence, the sum of the given sequence is "2485".