Question 143

If $$1^3 + 2^3 + .......... 10^3 = 3025$$, then the value of $$2^3 + 4^3 + .......... + 20^3$$ is:

Solution

Given : $$1^3 + 2^3 + .......... 10^3 = 3025$$ -------------(i)

To find : $$2^3 + 4^3 + .......... + 20^3$$

= $$(2\times1)^3 + (2\times2)^3 + .......... + (2\times10)^3$$

= $$(8\times1^3)+(8\times2^3)+ ............+ (8\times10^3)$$

= $$8\times(1^3+2^3+ ...............+ 10^3)$$

Substituting value from equation (i), we get :

= $$8\times3025=24200$$

=> Ans - (C)

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