Solution: 13+13+1100+ +13+899100=∑n=089913+n10013=13+1100=13+2100= =13+65100=013+66100= =13+165100=1100 times=10013+166100= =13+265100=2100 times=20013+266100= =13+365100=3100 times=30013+366100= =13+465100=4100 times=40013+466100= =13+565100=5100 times=50013+566100= =13+665100=6100 times=60013+666100= =13+765100=7100 times=70013+766100= =13+865100=8100 times=80013+866100= =13+899100=933 times=297∑n=089913+n100=100+200+300+400+500+600+700+800+297=3897â€‹

Q 4 pls . .

Solution:

[\frac{1}{3}] + [\frac{1}{3} + \frac{1}{100}] + . . . + [\frac{1}{3} + \frac{899}{100}] = \sum_{n = 0}^{899} [\frac{1}{3} + \frac{n}{100}] [\frac{1}{3}] = [\frac{1}{3} + \frac{1}{100}] = [\frac{1}{3} + \frac{2}{100}] = . . . = [\frac{1}{3} + \frac{65}{100}] = 0 [\frac{1}{3} + \frac{66}{100}] = . . . = [\frac{1}{3} + \frac{165}{100}] = 1 (100 times) = 100 [\frac{1}{3} + \frac{166}{100}] = . . . = [\frac{1}{3} + \frac{265}{100}] = 2 (100 times) = 200 [\frac{1}{3} + \frac{266}{100}] = . . . = [\frac{1}{3} + \frac{365}{100}] = 3 (100 times) = 300 [\frac{1}{3} + \frac{366}{100}] = . . . = [\frac{1}{3} + \frac{465}{100}] = 4 (100 times) = 400 [\frac{1}{3} + \frac{466}{100}] = . . . = [\frac{1}{3} + \frac{565}{100}] = 5 (100 times) = 500 [\frac{1}{3} + \frac{566}{100}] = . . . = [\frac{1}{3} + \frac{665}{100}] = 6 (100 times) = 600 [\frac{1}{3} + \frac{666}{100}] = . . . = [\frac{1}{3} + \frac{765}{100}] = 7 (100 times) = 700 [\frac{1}{3} + \frac{766}{100}] = . . . = [\frac{1}{3} + \frac{865}{100}] = 8 (100 times) = 800 [\frac{1}{3} + \frac{866}{100}] = . . . = [\frac{1}{3} + \frac{899}{100}] = 9 (33 times) = 297 \sum_{n = 0}^{899} [\frac{1}{3} + \frac{n}{100}] = 100 + 200 + 300 + 400 + 500 + 600 + 700 + 800 + 297 = 3897

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