Find the sum of :- $2017(2017^{100}) + 2016(2017^{101} + 2017^{102} + ... + 2017^{2016})$.
What I Tried :- I notice this is the same as :- $$2017(2017^{100}) + 2016(\sum_{n=101}^{2016} {2017^n})$$ $$\rightarrow 2017^{101} + 2016(2017^{101}) + 2016(\sum_{n=101}^{2016} {2017^n})$$ $$\rightarrow 2017(2017^{101}) + 2016(\sum_{n=101}^{2016} {2017^n})$$
Now how will I proceed. I am most annoyed with this problem because it has got unusual summations and multiplied in different no. of times.
Can Anyone help?
Hint :
Using $2016=2017-1$ everywhere should suffice.